text:
Talk:Mullah

Photograph; clergy
The photograph is inappropriate and/or inappropriately titled; it can best be said to show "A Muezzin giving the call to prayer." —iFaqeer | Talk to me! 20:56, Oct 12, 2004 (UTC)

 * Thank you to whoever changed the title.

 * Isn't the word "prophetically" a POV? And/or inaccurate—the quote describes reality as it was, not what change might happen. —iFaqeer | Talk to me! 21:54, Oct 22, 2004 (UTC)

'clergy' isn't really appropriate either as it connotes something similar to what the christian church uses.

 * The Term clergy can be used for any religious or political term. The christian church isnt just the only one. That is an offensive statement  —Preceding unsigned comment added by 199.172.211.7 (talk) 00:57, 22 April 2010 (UTC)

Recent removals
Someone had added a personal essay on popular use of the term "mullah", one that was strongly anti-Salafi and completely unreferenced. I removed it. I also removed a recently created template that is just very very bad. Too long, too detailed, completely incomprehensible to non-Muslims (and probably to many uneducated Muslims as well). Plus it completely unbalanced the formatting -- it was longer than the article! Template needs work. Zora 09:35, 4 February 2007 (UTC)

Still a stub?
Feel free to disagree with me, but I dont think this is a stub any more. Should it be removed from the stubs catagory and have the stub banner at the bottom removed? -Scaeme 17/05/07

Interwiki's not visible on page
The Interwiki's not visible on this page. Any idea why? Wiki-uk (talk) 14:19, 14 August 2008 (UTC)

something's wrong with this page
The sections do not have "edit" on their top right corner.. instead, all the "edits" are clustered at the right in the section "see also", I dont know how this happened and how to correct it Lilaac (talk) 19:10, 20 May 2009 (UTC)

Use as a derogatory term
This section might need expanding because it seems like people in Malta use the term "mullah" to mean... something. I honestly can't quite understand what it means but it definitely seems to be cropping up a lot regarding politics and it seems to be used in a derogatory tone. EG: http://www.timesofmalta.com/articles/view/20110516/opinion/Mullahs-in-the-control-room.365513

In trying to figure out the slang meaning I also came across this: http://www.urbandictionary.com/define.php?term=mullah I have no idea if that's widespread enough in America to warrant inclusion. Omgplz (talk) 12:10, 16 May 2011 (UTC)

The word is mispelled at Mullah. It is actually Mulla. — Preceding unsigned comment added by 71.234.194.44 (talk) 19:37, 24 February 2012 (UTC)
 * Nope, not in common usage English it isn't.HammerFilmFan (talk) 15:02, 4 December 2012 (UTC)

 * India has 2nd largets muslim population and Mulla/MUllah and Katwa are widespread and well known slur in India. Please include it. 58.182.172.95 (talk) 21:04, 11 January 2020 (UTC)

Mullah vs Ulama
Need to clarify the difference in the lead between a Mullah and an Islamic Scholar (Ulama). --Inayity (talk) 19:29, 3 December 2013 (UTC)
 * Ulama is actually plural. I believe the singular is allameh, as in Allameh Tabataba'i. Kanjuzi (talk) 04:47, 27 February 2019 (UTC)

Mullahs and Sunnis
Are there Sunni mullahs in the Middle East, or are they all Shias? The article is not clear whether there are Sunni mullahs in countries other than those on the Indian subcontinent. Clarification is needed. --P123ct1 (talk) 08:35, 11 July 2014 (UTC)

Note for the page
Just a note reminding everyone that fundamentalists are abusing the Quran & Haddiths. https://en.wikipedia.org/wiki/Fundamentalism might be improved by giving an example and why those who abuse the message aren't being true to their professed faith. http://www.pajhwok.com/en/2016/12/19/taliban-gun-down-badghis-woman-marrying-2-men being decent human beings unites us, not divides us. I am a Bahá'í - please don't think I wish to insult. — Preceding unsigned comment added by 81.99.74.135 (talk) 16:40, 19 December 2016 (UTC)

Unsuitable photo?
Can you explain why the image you deleted (a molla praying at a shrine in Tabriz) seems to you unsuitable? I didn't add it myself, but it seems to me perfectly appropriate, showing a typical Iranian mulla, in typical dress, engaged in a typical activity such as you may see every day in Iran. The article is poorer without it. Kanjuzi (talk) 05:00, 27 February 2019 (UTC)

Hanging Quote (Re: "Although ... interpret Islam". Source #12)
Whoever posted this did not really explain the quote included nor who said it, so it seems really out of place.

It's the last sentence in the last paragraph of the introduction.

There are also some issues with neutrality. The quote is very obviously anti-mullah. Not to mention that we shouldn't explain something in terms of another term until a solid background knowledge has been established first. — Preceding unsigned comment added by Danmusa562 (talk • contribs) 04:25, 20 January 2020 (UTC)

info on usage among shia
"Outside of Eastern Arabia, which has a long Shiite tradition and numerous Shiite minorities, the term is seldom used in other Arabic-speaking areas where its nearest equivalent is often shaykh (implying formal Islamic training), imam (prayer leader; not to be confused with the imams of the Shiite world), or ʿālim ("scholar", plural ʿulamāʾ). In the Sunni world, the concept of "cleric" is of limited usefulness, as authority in the religious system is relatively decentralized.[citation needed]"

To clarify the usage in Eastern Arabia: Mullah and Shaykh are different titles. Mullah is a clergyman who has not gone through formal Islamic training. "Imam" is only ever used in the very narrow context of referring to the prayer leader as a functional description, unlike among Sunnis where it is used sometimes as a honorific. — Preceding unsigned comment added by High surv (talk • contribs) 20:18, 20 November 2020 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Mullah


text:
Wikipedia:Articles for deletion/Something Awful Forums

 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result of the debate was - kept

Something Awful Forums
This seems far far too small a subject and far too localized to justify such a massive article on Wikipedia. Considering other major forums like GameFAQs, etc. are only described briefly in their parent article, this doesn't really belong as very nonencyclopedic.-- Etaonish 20:57, Oct 12, 2004 (UTC)

 * Keep. The size, scope and popularity of the forums seem large enough to warrant its own page. --Klo 04:36, 18 Oct 2004 (UTC)

 * Keep. If Wikipedia can have a detailed article about Slashdot trolls, then why not the SA forums? 24.229.95.152 16:57, 17 Oct 2004 (UTC)

 * Keep. Although not a "goon" myself, found the article interesting. Isn't the Something Awful Forums something like the #6 most popular forum on the Internet? The forums themselves have expanded beyond the original Something Awful website into an entity of their own, a hub of Internet culture. I do think the article is very specific and detailed, perhaps overly so, but it's not harming anyone to contain so much data. I'm not entirely opposed to moving the content to the Something Awful writeup, though I do see the validity of keeping it in its own article. --Jonathan Drain 23:44, 13 Oct 2004 (UTC)

 * Delete and Redirect: I quite agree. Let the Something Awful article serve, if service is needed.  We're not in the business of being a web guide, or a TV guide, or a record guide, IMO. Geogre 21:13, 12 Oct 2004 (UTC)
 * Keep. This used to be a large part of the Something Awful article. It got too big; it was split. Now you propose shoving it back in again. Nothing doing. There is far, far too much information to merge, which is why it was split in the first place. --Golbez 21:16, Oct 12, 2004 (UTC)
 * This is a very good point by Golbez. If an article must be split because its long, its child articles shouldn't be VfD'd.  Thus all votes asking for merge/redirect should probably just be considered "keep" (Since it would have to be split off again anyways)  — siro  χ  o  19:31, Oct 13, 2004 (UTC)
 * Merge/redirect. [[User:Neutrality|Neutrality (hopefully!)]] 21:29, Oct 12, 2004 (UTC)
 * Kill it. Delete.  Non-encylopedic l33t wanking over distinctly non-funny or important forum.  Oh, and tl;dr .  Terrapin 21:33, 12 Oct 2004 (UTC)
 * This voter seems to have a vendetta against the topic. The article clearly encyclopedic  (just read it, and look up the definition of encyclopedic while you're at it).  The forum is very popular, "important" is a POV, and its level of funniness does not matter.  — siro  χ  o
 * Keep. Major forum with a lot of information in the article. - RedWordSmith 21:39, 12 Oct 2004 (UTC)
 * Keep. Incredibly, Wikipedia doesn't just cover stuff that you, personally, are interested in. --Twinxor 21:46, 12 Oct 2004 (UTC)
 * We've had a lot of these lately, where a few users decide that having a quality article on a niche topic is somehow unnacceptable, and then everyone rushes to defend it. Whatever what you think of Wikipedia's scope, it's not useful to have a detailed, well-written article deleted. --Twinxor 22:19, 12 Oct 2004 (UTC)
 * Amazingly enough, I've proposed one VfD so far. This one.  I don't do this to any article I don't care about: I do this to any article that I feel is nonencyclopedic and quite useless to Wikipedia as a whole.  How many people do you think would genuinely care about this?  We've had the same debate over the GameFAQs forum histories: that eventually was completely deleted over my objections.  If GameFAQs doesn't deserve it, what makes you think SA is so important that they warrant a special wiki entry?  It's not even close to being one of the more active message boards online anyway. Plus, your argument can be applied to anything: you should also argue for the inclusion of a hyperdetailed article on my personal life under Edward Fu.  It can be a quality article on a niche topic, but it's unacceptable all the same. -- Etaonish  01:01, Oct 13, 2004 (UTC)
 * This isn't about GameFAQs. It's about Something Awful Forums, like the big bar at the top of the edit box says. --Golbez 01:07, Oct 13, 2004 (UTC)
 * Congratulations for not being able to pick up any analogy at all, and also for completely ignoring everything else I had said. "If GameFAQs doesn't deserve it, what makes you think SA is so important that they warrant a special wiki entry?" Considering not even Slashdot gets this much coverage. -- Etaonish  01:38, Oct 13, 2004 (UTC)
 * There is no analogy with GameFAQs. GameFAQs is a bunch of 12-year-olds trading catchphrases and potty humour; Something Awful is extremely intellectual (check out their Debate & Discussion forum) and produces a lot of content. Ashibaka ✎ 12:08, 13 Oct 2004 (UTC)
 * Who died and appointed you to judge whether or not an internet forum is "intellectual" vs "12-year-olds"? The two are equal in activity, the only objective criteria that matters.  Not to mention what a gross stereotype you cling to. (Oh, and, by the way, you don't seem to realize that anyone under 13 is banned from GameFAQs due to federal law)-- Etaonish  13:09, Oct 13, 2004 (UTC)
 * So they say. Ashibaka ✎ 17:10, 13 Oct 2004 (UTC)
 * Clearly you're not a GameFAQs user: else you can see for yourself. Dozens of people get banned for even joking about their age.  That's irrelevant anyway.-- Etaonish  18:16, Oct 13, 2004 (UTC)
 * I don't really understant – as a result of losing the GameFAQs battle, you decided to go delete other stuff? The thing is, encyclopedic-ness is pretty subjective. Seems to me that SA is one of the more influential forums out there, as evidenced by the memes it spawns and the thousands who have paid for membership. --Twinxor 03:09, 13 Oct 2004 (UTC)
 * Face reality: SA is NOT highly important to the Internet's community. Alexa ranking of 4608 for the main site? Also, you've misunderstood me: I learned from the GameFAQs battle exactly why our large articles were considered inappropriate for Wikipedia.  That's why I've carried it over to this article: it's a waste of resources to list every single forum in all of SA.  Encyclopedicness is actually rather objective: In 100 years, will anyone care about FYAD 2.0?  You also never answered my post earlier.-- Etaonish  13:09, Oct 13, 2004 (UTC)
 * Keep. Very significant web forum and too large to properly merge.  --Goobergunch 21:57, 12 Oct 2004 (UTC)
 * Keep. Significant forum, well written article, too big to merge. --Neschek 22:11, 12 Oct 2004 (UTC)
 * Merge only the content above the ToC into the Something Awful article, then redirect. -Sean Curtin 01:14, Oct 13, 2004 (UTC)
 * Keep, and start enforcing the guidelines about what should be listed for deletion. Mark Richards 03:17, 13 Oct 2004 (UTC)
 * Delete. Not notable. --Improv 04:18, 13 Oct 2004 (UTC)
 * Keep as some of the most notable forums on the internet. — siro  χ  o  04:54, Oct 13, 2004 (UTC)
 * Merge / Redirect with Rewrites back into Something Awful. It's pretty pathetic, in a way, that a website can have two fairly lengthy articles written about it that are larger than some articles about major cities.  Additionally, articles that contain large indexes of "common terms from the website" don't seem to be very "encyclopedic" in the strictest sense.. many of the terms listed are common on a variety of message boards, not just exclusively SAForums (many of them are used routinely on FARK and others). To those who say "too large to merge", maybe the article on Something Awful needs to be shorter in general.. Wikipedia Is Not A Webguide.  --feedle 05:56, 13 Oct 2004 (UTC)
 * Keep, strongly. Possibly the most famous, notorious, and notable internet forums. (For the record, I'm not a user there, so I have no vested interest, not that anyone was accusing.) Well-written and extensive articles on niche, fringe, and pop-culture topics are one of the major things which make IMO Wikipedia a superior reference tool to Britannica, et al. Gamaliel 06:34, 13 Oct 2004 (UTC)
 * Keep. This is ridiculous. This is the most famous and popular Internet forum in the United States, and if 2ch deserves an article for being the most famous in Japan, then SA certainly deserves an article too. Ashibaka ✎ 12:04, 13 Oct 2004 (UTC)
 * To both of you above: does 2ch have a subsection on all of its forums? I'm not asking for the SA article to be deleted: I'm asking for that useless stack of SA forum descriptions (FYAD 2.0, for example) to be removed as unencyclopedic.  In addition, it is NOT the most famous and popular Internet forum.  Strictly based on posts, it has ~19 million compared to ~18 million for GameFAQs; its Alexa ranking is 4608 while GameFAQs is 791.-- Etaonish  13:09, Oct 13, 2004 (UTC)
 * Oh, so we should remove some of the content? Are you suggesting a maximum length for articles? Ashibaka ✎ 17:10, 13 Oct 2004 (UTC)
 * No set maximum, obviously, but there's a reasonable limit on how much detail it is worth going into. This much detail on such an insignificant site is unneeded.-- Etaonish  18:24, Oct 13, 2004 (UTC)
 * Comment: Most of the non-Keep comments are comparing the article with others on Wikipedia. So far as I know, this is not how VfD works. VfD looks at each article on its own merits, not compared with others. We don't say "Well all the other articles on X subject are stub-length, so why should this get two full-sized articles," or "Its Alexa rating is lower than other sites, therefore its article must be smaller." We use independent thought and judge each article on its own merits. Just because SA has more text dedicated to it than most major cities is not a reason for deletion - it's a reason for you to stop complaining and add more information to those cities. --Golbez 14:09, Oct 13, 2004 (UTC)
 * Actually, I am measuring it on its own merits by comparing it to other sites. GameFAQs was cut down after a long debate; since it is more important than SA therefore SA should be cut down.  Makes sense to me.  Plus, the reason the city articles are shorter than SA isn't because the city articles are bad or short at all, it's because SA is disproportionately long.  That's the key: compared to other worthwhile subjects, the SA forums is too detailed on too small a subject matter.
 * Above was said by Etaonish. BTW, since when did # of bytes said on a particular subject equate with the importance of said subject? --Golbez 15:10, Oct 13, 2004 (UTC)
 * Since Wikipedia was created. Encyclopedias don't labor over minute inane details, neither should we.-- Etaonish  18:16, Oct 13, 2004 (UTC)
 * Then why are you? --Golbez 18:52, Oct 13, 2004 (UTC)
 * Comment: My reasonings behind my Merge / Redirect had little to do with comparing it to other articles (although my flippant remark about it being larger than some entries for major cities remains: if people put this much energy into the entry for their hometowns, Wikipedia would certainly be the better for it). The reality is, much of the information there could be rewritten in a more encyclopedic format, and the information regarding commonly used terminology on the forums applies to many online forums, not just SA.  Longer articles don't always mean "more informative".  Some of what is in the Forums article reads like fanboy cruft, and may in fact contain much that could be considered apocryphal. --Feedle 17:16, 13 Oct 2004 (UTC)
 * Keep: I've heard of Something Awful for years -- it's been floating around on the periphery of my Net conciousness for as long as I can remember. I read this article with interest.  It explains a lot about a Web site and set of forums that has a lot of saturation around the Web.  I see value here, if only for the fact that I personally found it valuable and I'm as typical a Net surfer as you're gonna find. --Deane 15:42, Oct 13, 2004 (UTC)
 * Keep: The article is too large to re-merge with the main article. --Mr VacBob
 * Delete: fancruft. Wile E. Heresiarch 15:53, 13 Oct 2004 (UTC)
 * Keep: The article is long, but its very informative throughout. I enjoyed reading it. Finally I understand all the talk about this website and especially the forums. --irrsinn
 * Merge / Redirect with Rewrites : It needs some major reworking into a more concise form that could be integrated into the Something Awful article. Most of the current page consists of information that would better belong in a Something Awful FAQ or a more general piece on Internet Culture. --BesigedB 18:41, 13 Oct 2004 (UTC)
 * Keep: With retrospect, I would agree with Golbez's view on what this page is for. --BesigedB 19:06, 13 Oct 2004 (UTC)
 * That would be a correctible flaw, anyway, not a cause to remove the entire page. --Mr VacBob
 * Comment: Incidentally, the whole of SomethingAwful's presence on Wikipedia is ~42k. I barely counted half of the articles primarily related to New York City, and those totalled up to ~179kb. Budapest, sadly, lags with only 14k. But do we not write about what we know? I have no problem with pruning this page at all - perhaps, even, in the future, remerging it with SA. But that is not what VfD is for. We do not vote here to prune. We vote here to delete, or to do an immediate merge. Yes? --Golbez 18:52, Oct 13, 2004 (UTC)
 * keep Cabalamat 22:02, 13 Oct 2004 (UTC)
 * Trim/Delete: The article itself is informative if the reader has a casual interest in SA, however it goes into way too much detail. Yes, the forums are large and each has it's own unique merits but if people want to know the specifics and the history of the forums, then can goto SA for that. There is a wealth of such detailed information in the "SAclopedia". It's a shame to lose the time and effort someone has put into writing it, but it's really just too much of a niché subject to deserve such detail. --62.190.225.1 23:44, 13 Oct 2004 (UTC)
 * Wiki is not paper. --Ian Maxwell 05:04, 2004 Oct 14 (UTC)
 * Keep. silsor 23:51, Oct 13, 2004 (UTC)
 * Keep The article is informative, and a useful resource for people that might be interested in joining the forums, but are on the fence as to whether they want to toss their $10 into the abyss or not. Some downsides about the forums could stand to be made in the article, but in a civil manner and not in a way percieved as vandalism.  --BonzoESC 02:04, 14 Oct 2004 (UTC)
 * Absolutely keep. I have read this article from start to finish a few times and I had never even been to the forums (though had been to the site). While I'm not one for bandwagon appeals, the sheer number of responses here should speak to the level of interest in the article. --Ian Maxwell 05:04, 2004 Oct 14 (UTC)
 * Keep. --Fastfission 06:01, 14 Oct 2004 (UTC)
 * Will be Trimmed, Redirected and Merged once VFD period is over. Be bold.  This is ridiculous, a 6,000 word article (read that again) about a forum that is ALREADY mentioned in the Something Awful article.  The fact that the sockpuppets are out in force tells me all I need to know.  Terrapin 14:28, 14 Oct 2004 (UTC)
 * That's a serious accusation, Terrapin, and I don't like your dictatorial attitude. You should still be bound by the vote.  If you are accusing users of cheating, at least have the decency to accuse them by name.  Keep.  --L33tminion 18:46, Oct 14, 2004 (UTC)
 * Tell you what, I'll change my vote to keep if SA posts more Leonard Crabs "faux lawyer" emails to litigious idiots. Those make me LMAO. Terrapin 21:13, 14 Oct 2004 (UTC)
 * "sockpuppets" is kind of a ridiculous declaration, don't you think, considering that this exactly the kind of vote which strangers would come to vote on? Good thing this isn't receiving much attention on the Something Awful forums themselves, because then you would have hundreds of votes from newcomers, all of whom no doubt would be "sockpuppets" according to you. silsor 19:32, Oct 14, 2004 (UTC)
 * Isn't it official Wikipedia policy to ban this from happening? Dozens of users registering simply to votespam?-- Etaonish  21:12, Oct 14, 2004 (UTC)
 * Each user is entitled to one vote each. However, the 100 edit rule might suggest that a user who signs up and make their first action to place a vote, should not have his vote weigh quite as much.--Jonathan Drain 21:30, 14 Oct 2004 (UTC)
 * Terrapin, if you think I'm a sockpuppet I've got [21C!s at Everything2] that suggest otherwise.--Jonathan Drain 21:30, 14 Oct 2004 (UTC)
 * Why did you do this before the discussion period ended? MrVacBob 01:42, 17 Oct 2004 (UTC)

 * Keep. I'll refrain from further comment here. Kim Bruning 19:01, 14 Oct 2004 (UTC)

 * Keep. Normally I'd vote merge/redirect, except that this was split off due to length. It may need to be cut down to focus less on trends only interesting to "goons", but that's tangential to VfD. People (on both sides of the debate) need to calm down, as some comments are getting perilously close to personal attacks.   — Gwalla | Talk 22:50, 14 Oct 2004 (UTC)

 * Delete or at least severely trim/merge/redirect. Concur with Wile E. Heresiarch: this is fancruft. jni 13:27, 17 Oct 2004 (UTC)

 * Delete. Forums don't deserve pages of their own. This is just plain fancruft. --Andylkl 14:17, 19 Oct 2004 (UTC)

Discussion

 * Alert: Both Irrsinn and Mr VacBob are very clearly sockpuppets, user accounts created solely to vote here.  I ask: is this the product of an "intellectual" forum, so desperate that they are creating new accounts on Wikipedia to votespam here?-- Etaonish  18:22, Oct 13, 2004 (UTC)
 * Note: MrVacBob's account was started on 22 Aug 2004, well before this vote began. There are 9 out of 15 total contributions that are unrelated to this vote, 7 of which were made (all to SA or SAF) before the vote began. Despite having a "red" name, Jonathan Drain's account was started well before this vote began, 8 Sep 2004. He has a total of 25 out of 39 edits unrelated to this vote, 17 of which were made before this vote began. func(talk) 04:44, 15 Oct 2004 (UTC)
 * Such appeals do not help your case, Etaonish. --Golbez 18:52, Oct 13, 2004 (UTC)
 * So your response is that I'm a gimmick account of someone else? Perhaps you should use Google. I'm certainly not going to actively bother to disprove that, since I doubt anyone else believes the claim. --Mr VacBob
 * Do some basic research before making such outrageous claims. Google would be a good start. Ashibaka ✎ 23:08, 13 Oct 2004 (UTC)
 * I can voice for MrVacBob's legitimacy; I've known him on IRC for quite a while now.--Jonathan Drain 23:11, 13 Oct 2004 (UTC)
 * I apologize for using an inappropriate word. What I meant was that the account was almost certainly created because of this controversy hence ought not to be given much weight.  That is standard wiki policy: see the 100-edit rule.-- Etaonish  00:04, Oct 14, 2004 (UTC)
 * Yes infact I did sign up after I read this article and noticed it was up for deletion. I had no reason to sign up before. I don't write articles on wikis in my second language. Also I'm not a member at somethingawful, i wouldn't pay for that. --irrsinn 19:20, Oct 14, 2004 (GMT)
 * Rewrite into : the article is also blatantly inserting dubious claims: like the section on 'ZOMG', which says "Rick (real name Matthew Milan) and hannibal (2nd. Lt. James "Turbo" Curbo) are its creators; others who claim to have coined it are lying.)". Do you really think that were it not for SA, no one would be using that phrase?  It's been independently invented many times over before and after SA.  This article has to be cut down to a reasonable level, if not simply deleted completely.-- Etaonish  18:22, Oct 13, 2004 (UTC)
 * Yeah, because "ZOMG" is a common typo. 24.91.125.90 23:14, 13 Oct 2004 (UTC)
 * Yeah, because no one could have ever thought of something like "ZOMG". It's not very difficult to think of something like that. I used it very early on in my internet career in instant messaging with no outside influence.-- Etaonish  00:04, Oct 14, 2004 (UTC)
 * I will agree that a four-letter Internet word is not very important to the dictionary, but this post is the first occurance of the word on Usenet, and is being used by one of the aforementioned people. It may be an accurate claim. (edit: there is a single use in 1999, but it only begins to be used more frequently after the linked post) -- Mr VacBob
 * I can't tell if 24.91.125.90 is being serious or not here, but I challenge anyone who says that ZOMG existed prior to Curbo and Milan's creation of it in January 2003, to bring forth evidence. The Something Awful Forums can be surprisingly effective as a means of spreading memes, especially with its links to 4chan. I will, however, concede that the "others who claim to have coined it are lying" is a poor way of phrasing it. (Edit: I just found a 1999 usenet post which said ZOMG. I still hold that Curbo and Milan coined and popularized the phrase in spite of its earlier use.) --Jonathan Drain 23:36, 13 Oct 2004 (UTC)

 * Clarification So I'm Matthew Milan, and I did coin (or conversely, re-coin) ZOMG with James Curbo in January 2003.  It wasn't really an SA thing initially - James and I were both mods/ops in a DC hub called 'Raspberry Heaven', which was a very peripheral spin-off of SA.  James and I (along with other members of the hub) started using the 'word' to mock script kiddies and the like.  I was posting a lot in alt-raptors at the time, and it got used a lot in there as well by myself as the poor Raps went belly up that year.  Eventually it leaked out of the DC Hub into SA, where it spread into infamy.  For a while, I personally tried to promote its use to see how widespread it could become, but that was ages ago.  I'm sure people used ZOMG before we did. I'm sure people will use it in the future.  It's a stupid joke/experiment that stopped holding interest for me ages ago.  I will not miss it when it is gone. I am however, rather annoyed by Etaonish, who seems to be a complete fuckwad.  Dear Sir: Please shove your self-serving rhetoric up your own ass, you pretentious twatburger. Also, I can sell you zomg.com for a dollar if it stops your from whining.  --Matthew Milan

 * Comment: What irks me tremendously (though I assure you it has nothing to do with why I nominated SA forums) is that the exact same controversy erupted over the GameFAQs articles, and some of the users currently wanting to keep SA voted against keeping GameFAQs (this is a vague vague recollection, no formal accusation). GameFAQs was split; its board histories were then put up on VfD, upon which they remerged it with GameFAQs, and it was later completely chopped out of the article.  The primary reason no one protested was that there was a dearth of GameFAQs users on Wiki at the time.  But SA forums has a large base of SA goons on Wikipedia that will inevitably support its own article.

The SA Forums article is unencyclopedic for the same reasons a vanity page on myself is unencyclopedic: no one really cares about FYAD 2.0, a forum that lasted all of one day. This is obscurity painted as something that actually matters to Wikipedia. I have no vendetta against SA; rather, the SA goons have a vendetta against anyone remotely anti-SA.

Back to Golbez's point. SA was split, but that doesn't mean the material in the child articles was good. The material in SA forums is *inherently* unneeded and should have never led to the split of the original SA article in the first place. Golbez presumes that the material that ballooned the original SA article was needed, when in fact it should have led to it being removed rather than splitting the article in two.

SA then argues that the main reason it belongs on Wiki rather than GameFAQs is because they are more "intellectual", they somehow are "better" than a bunch of "12-year-olds". I claim that using that argument in and of itself disproves their theory, but the real point is that you should only measure importance by objective factors. Objectively, SA is less important than GameFAQs due to its much lower Alexa rating and the fact that it has a tenth of its posts.

 * With respect, Etaonish, the Something Awful Forums requires payment to sign up (albeit a nominal amount) which dissuades casual posters and children from signing up, while dissuading users from making an ass of themselves since their membership is actually worth something. The average SA "goon" is between young adult and college age, while the GameFAQs forums appeals to fans of even childrens' video games. I give the example that GameFAQs members routinely vote Final Fantasy VII and its characters as the best in the site's online polls. This doesn't mean there aren't both intellectuals and childish members on each forum, mainly that the average Something Awful Forums-goer is older, mentally older and smarter than the average GameFAQs forumgoer. I dare say that quantity is not better than quality when it comes to content; you need only view Something Awful's consistently humorous "Photoshop Phriday" and "Comedy Goldmine" articles to judge the calibre of many of their members. --Jonathan Drain 23:58, 13 Oct 2004 (UTC)
 * Actually, if you take a look at the boards, it is usually FFVII that is criticized and decried as undeserving. What simply happens is that general people who visit the site tend to be younger and vote for FFVII, but they are irrepresentative of the boards theselves.  In addition, GameFAQs is the site of much intellectual discussion, and I personally find it much better than what I have seen of SA.-- Etaonish  00:04, Oct 14, 2004 (UTC)
 * Ah, then you're a user of the GameFAQs forums. In any case, I believe that the Something Awful Forums has actually overtaken its parent webpage in terms of fame and notoriety. As such, when I think of SA I think of the boards before the webpage; when I think of GameFAQs, the reverse is true, as I visit it most often to find game faqs.
 * ^^Jonathan Drain well, the point was, we're comparing the two board articles. The same thing happened to both.-- Etaonish  00:22, Oct 14, 2004 (UTC)
 * That's a generalization, both forums are different. Do you mean to say that both expanded beyond their parent articles? I see where you're coming from here, but the Something Awful forums is more than simply a forum linked to another website - it's an online community. The people there aren't just forumgoers, they're goons; they have their own subculture and camaraderie. The forums are more important than the page, not the other way around - despite the GameFAQs forums being more popular numerically (3,000 goons online right now versus ~5,500 GameFAQs forumgoers). In addition, I would find it difficult to consider Etaonish unbiased in this matter, since he's a GameFAQs member himself.--Jonathan Drain 00:48, 14 Oct 2004 (UTC)
 * Interestingly, the same logic applies to GameFAQs. The boards are now almost totally separate from the FAQs.  Please don't assume things about things you don't know much about.  And I can be perfectly NPOV even though I'm a GameFAQer.  See my other post. -- Etaonish  01:42, Oct 14, 2004 (UTC)
 * Incidentally, I'm a member of both forums, so like, what does that say about me? --Golbez 01:11, Oct 14, 2004 (UTC)
 * It means you're a twelve year old goon ;) Seriously though, what I mean to say is that from previous edits, it's clear that Etaonish has a bias against the Something Awful Forums. He's obviously not pleased that GameFAQs forums lost its own writeup, and, holding his own GameFAQs forums in higher esteem than the Something Awful Forums, (he rates their entry as highly as vanity writeups on non-famous individuals) requests the same fate for their writeup. --Jonathan Drain 01:27, 14 Oct 2004 (UTC)
 * I should also add that it's clear that the SA members who refer to the GameFAQs forums as "a bunch of twelve year olds" have clearly soured the reputation of their forums in Etaonish's eyes, who, as a GameFAQs forumgoer, would clearly take such a statement personally. --00:52, 14 Oct 2004 (UTC)
 * Correction: it means that I was a newb at the time of the GameFAQs deletion, and I have since realized and fought against people who repeatedly add random board history to the article. I voted for a controversial deletion of a LUEshi article, the main fad on the board that is just as notable as tl:dr.  Now I extend the policy to SA.  I assure you I have no bias against SA, in fact, I used to share an account with a person there before dropping it.  You are mistaken if you feel that my being a GameFAQer has anything to do with it.  (By the way, you were right, saying "a bunch of 12 year olds" does piss me off, but I know better than to seek Internet grudges.)-- Etaonish  01:42, Oct 14, 2004 (UTC)

In short, either all of these forum articles ARE encyclopedic, upon which any remotely popular internet forum deserves a Wikipedia article devoted to its history and traditions and fads, or all of these forum articles are NOT encyclopedic, upon which the SA forums deserve no more than a mention and some objective material about when it was created, etc.

(posted on Siroxo's talk page) -- Etaonish 21:08, Oct 13, 2004 (UTC)

No, it's not an all or nothing proposition. Each decision is made on a case by case basis. This is precisely why we have a discussion forum here at VfD instead of merely a deletion checklist. All forums should not be included or excluded, just like we don't include or exclude all books, people, institutions, TV shows, etc.

I also don't think the relative Alexa ranking of SA vs. GameFAQs is relevant. Of course we should take it into account, and SA's ranking is rather high I understand. But notability is not just ratings or rankings. SA has an influence and noteriety far beyond its rankings, one which I don't believe GameFAQs has despite its higher traffic. (SA's part in the propigation of the All Your Base meme, for example.) I would compare SA to television shows like Twin Peaks, Buffy, or the original Star Trek, much discussed shows which are far more notable than shows which far outstriped their ratings, crap like One Tree Hill or Charmed which are far less notable and will be quickly forgotten. Gamaliel 06:08, 14 Oct 2004 (UTC)

 * Actually, it's relevant because there is really no other way to objectively measure influence. Sites higher up on Alexa are more important.  Obviously trivial differences are irrelevant, but when there is such a huge gap (4608 vs 791, and keep in mind this is people who visit ANY part of the site of SA), it clearly shows that the more popular site is more influential.  (BTW, according to the official AYB history, it wasn't SA, but rather Overclocked that was mainly responsible http://www.planettribes.com/allyourbase/story.shtml#hist -- Etaonish  16:46, Oct 14, 2004 (UTC)
 * Numerical popularity is the only thing measured in pagehits, not relevance or influence. However, even so, we should take the Alexa figures in context. Gamefaqs shares Alexa count (#791) with its own boards, likewise, SA shares Alexa count (#4,608) with its own boards. Gamefaqs has a huge number of pages, being a website about pretty much every single game and game system ever, with at perhaps thirty or more FAQs on any popular recent game. Conversely, Something Awful's main page is updated only once daily at best, and its forums are paid registration only, limiting the number of pages and visitors it appears to have. I'm not disputing the popularity of the GameFAQs forums, I'm merely saying that it's not quite the subculture that makes the Something Awful Forums an internet phenomenon in itself. --Jonathan Drain 22:03, 14 Oct 2004 (UTC)
 * This is a more accurate history: http://frogstar.com/aybabtu/aa-history.asp -- Mr VacBob

 * Keep. The Something Awful Forums are a part of a lot of humor on the internet, with many internet meme's, catchprhases and other known nuances originating from those forums. To delete information that explains how these rather large forums operate wouldn't be in the best intrests of information preservation.

 * Keep and do not trim. This is one of the most popular forums on the internet, and worth every word.  If you don't like it that this article is longer than others on wikipedia, then add to those articles; don't take stuff away!  I really don't think that it's bad that this article is 60k long, as 60kb is not that much when one looks at the immensity of wikpedia.  And being able to extensively cover an internet forum shows how wikipedia can do stuff a paper encyclopedia could never get close to.-PlasmaDragon 15:22, 15 Oct 2004 (UTC)

Terrapin
You are NOT to unilaterally and pre-emptively perform a merge-redirect (Or rather, in your case, a simple redirect) on this article until AT LEAST the five-day VfD discussion period is over. My clock shows four days. Furthermore, no consensus has been made at all, and any such discussion will then belong on the talk pages. --Golbez 02:03, Oct 17, 2004 (UTC)

 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.


text:
1904 in Norwegian football

Results from the Football in Norway in 1904.

title: 1904 in Norwegian football


text:
Talk:Michael Dorris

Headline text
what is the book The Window about?

Contradictory
Dorris, born in Concord, NH to Jim and Mary Besy (Burkhardt) Dorris in Louisville, Kentucky, was of mixed Modoc Indian, Irish, and French blood. Okay born in Concord or Louisville, it could not have been both. He died in Concord I know that. —Preceding unsigned comment added by 66.30.220.220 (talk • contribs)

 * You're right -- though interestingly, Contemporary Authors Online says, "Born January 30, 1945, Louisville, KY (some sources say Dayton, WA)". I'll update and cite. Deborah-jl Talk 01:29, 3 March 2006 (UTC)

That still doesn't answer the question: was he born in Louisville, KY, Kansas City, or Dayton, WA? — Preceding unsigned comment added by 98.219.97.152 (talk) 23:10, 4 December 2012 (UTC)

Major expansion needed
Michael Dorris was an author first and foremost, and it's very wrong that the really quite horrible tragedy of his life is so firmly to the fore on this page. At the very least there should be summaries of The Broken Cord and A Yellow Raft in Blue Water here. Unfortunately, I haven't read either: could someone who has please expand this article's literary content? Vizjim 08:14, 31 March 2006 (UTC)

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as stub, and the rating on other projects was brought up to Stub class. BetacommandBot 16:32, 9 November 2007 (UTC)

Fair use rationale for Image:Louiseerdrich.jpg
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BetacommandBot (talk) 18:34, 2 January 2008 (UTC)

Correct Title
The reason there is no record of Mornin' Gurl is because Dorris' book is called Morning Girl. It won the Scott O'Dell Award. It is a wonderful children's book - every parent should read it to their children - especially their daughters. — Preceding unsigned comment added by 50.132.100.17 (talk) 21:01, 24 August 2012 (UTC)

External links modified (January 2018)
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 * Added archive https://web.archive.org/web/20120805123925/http://www.gf.org/fellows/results?competition=ALL&fellowship_category=ALL&lower_bound=1977&page=2&query=&upper_bound=1977 to http://www.gf.org/fellows/results?competition=ALL&fellowship_category=ALL&lower_bound=1977&page=2&query=&upper_bound=1977

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Father's suicide
Newsweek reports that "Dorris's own father committed suicide upon returning home from World War II. Michael learned about the suicide when he was in college, yet in a 1989 essay he said his father was killed on 'an icy mountain road' in Germany during the war." https://www.newsweek.com/death-native-son-171578 2601:647:6801:3C80:BD8D:E4CC:7FFB:B739 (talk) 01:28, 13 February 2024 (UTC)

title: Talk:Michael Dorris


text:
Associated Legendre polynomials

In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation

$$\left(1 - x^2\right) \frac{d^2}{d x^2} P_\ell^m(x) - 2 x \frac{d}{d x} P_\ell^m(x) + \left[ \ell (\ell + 1) - \frac{m^2}{1 - x^2} \right] P_\ell^m(x) = 0,$$

or equivalently

$$\frac{d}{d x} \left[ \left(1 - x^2\right) \frac{d}{d x} P_\ell^m(x) \right] + \left[ \ell (\ell + 1) - \frac{m^2}{1 - x^2} \right] P_\ell^m(x) = 0,$$

where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on $[−1, 1]$ only if ℓ and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial. When m is zero and ℓ integer, these functions are identical to the Legendre polynomials. In general, when ℓ and m are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions with arbitrary real or complex values of ℓ and m are Legendre functions. In that case the parameters are usually labelled with Greek letters.

The Legendre ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates. Associated Legendre polynomials play a vital role in the definition of spherical harmonics.

Definition for non-negative integer parameters $ℓ$ and $m$
These functions are denoted $$P_\ell^{m}(x)$$, where the superscript indicates the order and not a power of P. Their most straightforward definition is in terms of derivatives of ordinary Legendre polynomials (m ≥ 0)

$$ P_\ell^{m}(x) = (-1)^m (1-x^2)^{m/2} \frac{d^m}{dx^m} \left( P_\ell(x) \right), $$

The $(−1)^{m}$ factor in this formula is known as the Condon–Shortley phase. Some authors omit it. That the functions described by this equation satisfy the general Legendre differential equation with the indicated values of the parameters ℓ and m follows by differentiating m times the Legendre equation for $P_{ℓ}$: $$\left(1-x^2\right) \frac{d^2}{dx^2}P_\ell(x) -2x\frac{d}{dx}P_\ell(x)+ \ell(\ell+1)P_\ell(x) = 0.$$

Moreover, since by Rodrigues' formula, $$P_\ell(x) = \frac{1}{2^\ell\,\ell!} \ \frac{d^\ell}{dx^\ell}\left[(x^2-1)^\ell\right],$$ the P$m ℓ$ can be expressed in the form $$P_\ell^{m}(x) = \frac{(-1)^m}{2^\ell \ell!} (1-x^2)^{m/2}\ \frac{d^{\ell+m}}{dx^{\ell+m}}(x^2-1)^\ell.$$

This equation allows extension of the range of m to: $−ℓ ≤ m ≤ ℓ$. The definitions of $P_{ℓ}^{±m}$, resulting from this expression by substitution of $±m$, are proportional. Indeed, equate the coefficients of equal powers on the left and right hand side of $$\frac{d^{\ell-m}}{dx^{\ell-m}} (x^2-1)^{\ell} = c_{lm} (1-x^2)^m \frac{d^{\ell+m}}{dx^{\ell+m}}(x^2-1)^{\ell},$$ then it follows that the proportionality constant is $$c_{lm} = (-1)^m \frac{(\ell-m)!}{(\ell+m)!} ,$$ so that $$P^{-m}_\ell(x) = (-1)^m \frac{(\ell-m)!}{(\ell+m)!} P^{m}_\ell(x).$$

Alternative notations
The following alternative notations are also used in literature: $$P_{\ell m}(x) = (-1)^m P_\ell^{m}(x) $$

Closed Form
The Associated Legendre Polynomial can also be written as: $$ P_l^m(x)=(-1)^{m} \cdot 2^{l} \cdot (1-x^2)^{m/2} \cdot \sum_{k=m}^l \frac{k!}{(k-m)!}\cdot x^{k-m} \cdot \binom{l}{k} \binom{\frac{l+k-1}{2}}{l} $$ with simple monomials and the generalized form of the binomial coefficient.

Orthogonality
The associated Legendre polynomials are not mutually orthogonal in general. For example, $$P_1^1$$ is not orthogonal to $$P_2^2$$. However, some subsets are orthogonal. Assuming 0 ≤ m ≤ ℓ, they satisfy the orthogonality condition for fixed m:

$$\int_{-1}^{1} P_k ^{m} P_\ell ^{m} dx = \frac{2 (\ell+m)!}{(2\ell+1)(\ell-m)!}\ \delta _{k,\ell}$$

Where $δ_{k,ℓ}$ is the Kronecker delta.

Also, they satisfy the orthogonality condition for fixed $ℓ$:

$$\int_{-1}^{1} \frac{P_\ell ^{m} P_\ell ^{n}}{1-x^2}dx = \begin{cases} 0 & \text{if } m\neq n \\ \frac{(\ell+m)!}{m(\ell-m)!} & \text{if } m=n\neq0 \\ \infty & \text{if } m=n=0 \end{cases}$$

Negative $m$ and/or negative $ℓ$
The differential equation is clearly invariant under a change in sign of m.

The functions for negative m were shown above to be proportional to those of positive m: $$P_\ell ^{-m} = (-1)^m \frac{(\ell-m)!}{(\ell+m)!} P_\ell ^{m}$$

(This followed from the Rodrigues' formula definition. This definition also makes the various recurrence formulas work for positive or negative $m$.) $$\text{If}\quad |m| > \ell\,\quad\text{then}\quad P_\ell^{m} = 0.\,$$

The differential equation is also invariant under a change from $ℓ$ to $−ℓ − 1$, and the functions for negative $ℓ$ are defined by

$$P_{-\ell} ^{m} = P_{\ell-1} ^{m},\ (\ell=1,\,2,\, \dots).$$

Parity
From their definition, one can verify that the Associated Legendre functions are either even or odd according to

$$P_\ell ^{m} (-x) = (-1)^{\ell - m} P_\ell ^{m}(x) $$

The first few associated Legendre functions
The first few associated Legendre functions, including those for negative values of m, are:

$$P_{0}^{0}(x)=1$$

$$\begin{align} P_{1}^{-1}(x)&=-\tfrac{1}{2}P_{1}^{1}(x) \\ P_{1}^{0}(x)&=x \\ P_{1}^{1}(x)&=-(1-x^2)^{1/2} \end{align}$$

$$\begin{align} P_{2}^{-2}(x)&=\tfrac{1}{24}P_{2}^{2}(x) \\ P_{2}^{-1}(x)&=-\tfrac{1}{6}P_{2}^{1}(x) \\ P_{2}^{0}(x)&=\tfrac{1}{2}(3x^{2}-1) \\ P_{2}^{1}(x)&=-3x(1-x^2)^{1/2} \\ P_{2}^{2}(x)&=3(1-x^2) \end{align}$$

$$\begin{align} P_{3}^{-3}(x)&=-\tfrac{1}{720}P_{3}^{3}(x) \\ P_{3}^{-2}(x)&=\tfrac{1}{120}P_{3}^{2}(x) \\ P_{3}^{-1}(x)&=-\tfrac{1}{12}P_{3}^{1}(x) \\ P_{3}^{0}(x)&=\tfrac{1}{2}(5x^3-3x) \\ P_{3}^{1}(x)&=\tfrac{3}{2}(1-5x^{2})(1-x^2)^{1/2} \\ P_{3}^{2}(x)&=15x(1-x^2) \\ P_{3}^{3}(x)&=-15(1-x^2)^{3/2} \end{align}$$

$$\begin{align} P_{4}^{-4}(x)&=\tfrac{1}{40320}P_{4}^{4}(x) \\ P_{4}^{-3}(x)&=-\tfrac{1}{5040}P_{4}^{3}(x) \\ P_{4}^{-2}(x)&=\tfrac{1}{360}P_{4}^{2}(x) \\ P_{4}^{-1}(x)&=-\tfrac{1}{20}P_{4}^{1}(x) \\ P_{4}^{0}(x)&=\tfrac{1}{8}(35x^{4}-30x^{2}+3) \\ P_{4}^{1}(x)&=-\tfrac{5}{2}(7x^3-3x)(1-x^2)^{1/2} \\ P_{4}^{2}(x)&=\tfrac{15}{2}(7x^2-1)(1-x^2) \\ P_{4}^{3}(x)&= - 105x(1-x^2)^{3/2} \\ P_{4}^{4}(x)&=105(1-x^2)^{2} \end{align}$$ <!-- $$\begin{align} P_{5}^{-5}(x)&={1\over 3840}\left(\sqrt{1-x^2}\right)^{5} \\ P_{5}^{-4}(x)&={1\over 384}\left(\sqrt{1-x^2}\right)^{4}x \\ P_{5}^{-3}(x)&={1\over 384}\left(\sqrt{1-x^2}\right)^{3}(9x^{2}-1) \\ P_{5}^{-2}(x)&={1\over 16}\left(\sqrt{1-x^2}\right)^{2}(3x^{3}-1x) \\ P_{5}^{-1}(x)&={1\over 16}\left(\sqrt{1-x^2}\right)(21x^{4}-14x^{2}+1) \\ P_{5}^{0}(x)&={1\over 8}(63x^{5}-70x^{3}+15x) \\ P_{5}^{1}(x)&={-15\over 8}\left(\sqrt{1-x^2}\right)(21x^{4}-14x^{2}+1) \\ P_{5}^{2}(x)&={105\over 2}\left(\sqrt{1-x^2}\right)^{2}(3x^{3}-1x) \\ P_{5}^{3}(x)&={-105\over 2}\left(\sqrt{1-x^2}\right)^{3}(9x^{2}-1) \\ P_{5}^{4}(x)&=945\left(\sqrt{1-x^2}\right)^{4}x \\ P_{5}^{5}(x)&=-945\left(\sqrt{1-x^2}\right)^{5} \end{align}$$

$$\begin{align} P_{6}^{-6}(x)={1\over 46080}\left(\sqrt{1-x^2}\right)^{6} \\ P_{6}^{-5}(x)={1\over 3840}\left(\sqrt{1-x^2}\right)^{5}x \\ P_{6}^{-4}(x)={1\over 3840}\left(\sqrt{1-x^2}\right)^{4}(11x^{2}-1) \\ P_{6}^{-3}(x)={1\over 384}\left(\sqrt{1-x^2}\right)^{3}(11x^{3}-3x) \\ P_{6}^{-2}(x)={1\over 128}\left(\sqrt{1-x^2}\right)^{2}(33x^{4}-18x^{2}+1) \\ P_{6}^{-1}(x)={1\over 16}\left(\sqrt{1-x^2}\right)(33x^{5}-30x^{3}+5x) \\ P_{6}^{0}(x)={1\over 16}(231x^{6}-315x^{4}+105x^{2}-5) \\ P_{6}^{1}(x)={-21\over 8}\left(\sqrt{1-x^2}\right)(33x^{5}-30x^{3}+5x) \\ P_{6}^{2}(x)={105\over 8}\left(\sqrt{1-x^2}\right)^{2}(33x^{4}-18x^{2}+1) \\ P_{6}^{3}(x)={-315\over 2}\left(\sqrt{1-x^2}\right)^{3}(11x^{3}-3x) \\ P_{6}^{4}(x)={945\over 2}\left(\sqrt{1-x^2}\right)^{4}(11x^{2}-1) \\ P_{6}^{5}(x)=-10395\left(\sqrt{1-x^2}\right)^{5}x \\ P_{6}^{6}(x)=10395\left(\sqrt{1-x^2}\right)^{6} \end{align}$$

$$\begin{align} P_{7}^{-7}(x)&={1\over 645120}\left(\sqrt{1-x^2}\right)^{7} \\ P_{7}^{-6}(x)&={1\over 46080}\left(\sqrt{1-x^2}\right)^{6}x \\ P_{7}^{-5}(x)&={1\over 46080}\left(\sqrt{1-x^2}\right)^{5}(13x^{2}-1) \\ P_{7}^{-4}(x)&={1\over 3840}\left(\sqrt{1-x^2}\right)^{4}(13x^{3}-3x) \\ P_{7}^{-3}(x)&={1\over 3840}\left(\sqrt{1-x^2}\right)^{3}(143x^{4}-66x^{2}+3) \\ P_{7}^{-2}(x)&={1\over 384}\left(\sqrt{1-x^2}\right)^{2}(143x^{5}-110x^{3}+15x) \\ P_{7}^{-1}(x)&={1\over 128}\left(\sqrt{1-x^2}\right)(429x^{6}-495x^{4}+135x^{2}-5) \\ P_{7}^{0}(x)&={1\over 16}(429x^{7}-693x^{5}+315x^{3}-35x) \\ P_{7}^{1}(x)&={-7\over 16}\left(\sqrt{1-x^2}\right)(429x^{6}-495x^{4}+135x^{2}-5) \\ P_{7}^{2}(x)&={63\over 8}\left(\sqrt{1-x^2}\right)^{2}(143x^{5}-110x^{3}+15x) \\ P_{7}^{3}(x)&={-315\over 8}\left(\sqrt{1-x^2}\right)^{3}(143x^{4}-66x^{2}+3) \\ P_{7}^{4}(x)&={3465\over 2}\left(\sqrt{1-x^2}\right)^{4}(13x^{3}-3x) \\ P_{7}^{5}(x)&={-10395\over 2}\left(\sqrt{1-x^2}\right)^{5}(13x^{2}-1) \\ P_{7}^{6}(x)&=135135\left(\sqrt{1-x^2}\right)^{6}x \\ P_{7}^{7}(x)&=-135135\left(\sqrt{1-x^2}\right)^{7} \end{align}$$

$$\begin{align} P_{8}^{-8}(x)={1\over 10321920}\left(\sqrt{1-x^2}\right)^{8} \\ P_{8}^{-7}(x)&={1\over 645120}\left(\sqrt{1-x^2}\right)^{7}x \\ P_{8}^{-6}(x)&={1\over 645120}\left(\sqrt{1-x^2}\right)^{6}(15x^{2}-1) \\ P_{8}^{-5}(x)&={1\over 15360}\left(\sqrt{1-x^2}\right)^{5}(5x^{3}-1x) \\ P_{8}^{-4}(x)&={1\over 15360}\left(\sqrt{1-x^2}\right)^{4}(65x^{4}-26x^{2}+1) \\ P_{8}^{-3}(x)&={1\over 768}\left(\sqrt{1-x^2}\right)^{3}(39x^{5}-26x^{3}+3x) \\ P_{8}^{-2}(x)&={1\over 256}\left(\sqrt{1-x^2}\right)^{2}(143x^{6}-143x^{4}+33x^{2}-1) \\ P_{8}^{-1}(x)&={1\over 128}\left(\sqrt{1-x^2}\right)(715x^{7}-1001x^{5}+385x^{3}-35x) \\ P_{8}^{0}(x)&={1\over 128}(6435x^{8}-12012x^{6}+6930x^{4}-1260x^{2}+35) \\ P_{8}^{1}(x)&={-9\over 16}\left(\sqrt{1-x^2}\right)(715x^{7}-1001x^{5}+385x^{3}-35x) \\ P_{8}^{2}(x)&={315\over 16}\left(\sqrt{1-x^2}\right)^{2}(143x^{6}-143x^{4}+33x^{2}-1) \\ P_{8}^{3}(x)&={-3465\over 8}\left(\sqrt{1-x^2}\right)^{3}(39x^{5}-26x^{3}+3x) \\ P_{8}^{4}(x)&={10395\over 8}\left(\sqrt{1-x^2}\right)^{4}(65x^{4}-26x^{2}+1) \\ P_{8}^{5}(x)&={-135135\over 2}\left(\sqrt{1-x^2}\right)^{5}(5x^{3}-1x) \\ P_{8}^{6}(x)&={135135\over 2}\left(\sqrt{1-x^2}\right)^{6}(15x^{2}-1) \\ P_{8}^{7}(x)&=-2027025\left(\sqrt{1-x^2}\right)^{7}x \\ P_{8}^{8}(x)&=2027025\left(\sqrt{1-x^2}\right)^{8} \end{align}$$

$$\begin{align} P_{9}^{-9}(x)&={1\over 185794560}\left(\sqrt{1-x^2}\right)^{9} \\ P_{9}^{-8}(x)&={1\over 10321920}\left(\sqrt{1-x^2}\right)^{8}x \\ P_{9}^{-7}(x)&={1\over 10321920}\left(\sqrt{1-x^2}\right)^{7}(17x^{2}-1) \\ P_{9}^{-6}(x)&={1\over 645120}\left(\sqrt{1-x^2}\right)^{6}(17x^{3}-3x) \\ P_{9}^{-5}(x)&={1\over 215040}\left(\sqrt{1-x^2}\right)^{5}(85x^{4}-30x^{2}+1) \\ P_{9}^{-4}(x)&={1\over 3072}\left(\sqrt{1-x^2}\right)^{4}(17x^{5}-10x^{3}+1x) \\ P_{9}^{-3}(x)&={1\over 3072}\left(\sqrt{1-x^2}\right)^{3}(221x^{6}-195x^{4}+39x^{2}-1) \\ P_{9}^{-2}(x)&={1\over 256}\left(\sqrt{1-x^2}\right)^{2}(221x^{7}-273x^{5}+91x^{3}-7x) \\ P_{9}^{-1}(x)&={1\over 256}\left(\sqrt{1-x^2}\right)(2431x^{8}-4004x^{6}+2002x^{4}-308x^{2}+7) \\ P_{9}^{0}(x)&={1\over 128}(12155x^{9}-25740x^{7}+18018x^{5}-4620x^{3}+315x) \\ P_{9}^{1}(x)&={-45\over 128}\left(\sqrt{1-x^2}\right)(2431x^{8}-4004x^{6}+2002x^{4}-308x^{2}+7) \\ P_{9}^{2}(x)&={495\over 16}\left(\sqrt{1-x^2}\right)^{2}(221x^{7}-273x^{5}+91x^{3}-7x) \\ P_{9}^{3}(x)&={-3465\over 16}\left(\sqrt{1-x^2}\right)^{3}(221x^{6}-195x^{4}+39x^{2}-1) \\ P_{9}^{4}(x)&={135135\over 8}\left(\sqrt{1-x^2}\right)^{4}(17x^{5}-10x^{3}+1x) \\ P_{9}^{5}(x)&={-135135\over 8}\left(\sqrt{1-x^2}\right)^{5}(85x^{4}-30x^{2}+1) \\ P_{9}^{6}(x)&={675675\over 2}\left(\sqrt{1-x^2}\right)^{6}(17x^{3}-3x) \\ P_{9}^{7}(x)&={-2027025\over 2}\left(\sqrt{1-x^2}\right)^{7}(17x^{2}-1) \\ P_{9}^{8}(x)&=34459425\left(\sqrt{1-x^2}\right)^{8}x \\ P_{9}^{9}(x)&=-34459425\left(\sqrt{1-x^2}\right)^{9} \end{align}$$

$$P_{10}^{-10}(x)={1\over 3715891200}\left(\sqrt{1-x^2}\right)^{10}$$ $$P_{10}^{-9}(x)={1\over 185794560}\left(\sqrt{1-x^2}\right)^{9}x$$ $$P_{10}^{-8}(x)={1\over 185794560}\left(\sqrt{1-x^2}\right)^{8}(19x^{2}-1)$$ $$P_{10}^{-7}(x)={1\over 10321920}\left(\sqrt{1-x^2}\right)^{7}(19x^{3}-3x)$$ $$P_{10}^{-6}(x)={1\over 10321920}\left(\sqrt{1-x^2}\right)^{6}(323x^{4}-102x^{2}+3)$$ $$P_{10}^{-5}(x)={1\over 645120}\left(\sqrt{1-x^2}\right)^{5}(323x^{5}-170x^{3}+15x)$$ $$P_{10}^{-4}(x)={1\over 43008}\left(\sqrt{1-x^2}\right)^{4}(323x^{6}-255x^{4}+45x^{2}-1)$$ $$P_{10}^{-3}(x)={1\over 3072}\left(\sqrt{1-x^2}\right)^{3}(323x^{7}-357x^{5}+105x^{3}-7x)$$ $$P_{10}^{-2}(x)={1\over 3072}\left(\sqrt{1-x^2}\right)^{2}(4199x^{8}-6188x^{6}+2730x^{4}-364x^{2}+7)$$ $$P_{10}^{-1}(x)={1\over 256}\left(\sqrt{1-x^2}\right)(4199x^{9}-7956x^{7}+4914x^{5}-1092x^{3}+63x)$$ $$P_{10}^{0}(x)={1\over 256}(46189x^{10}-109395x^{8}+90090x^{6}-30030x^{4}+3465x^{2}-63)$$ $$P_{10}^{1}(x)={-55\over 128}\left(\sqrt{1-x^2}\right)(4199x^{9}-7956x^{7}+4914x^{5}-1092x^{3}+63x)$$ $$P_{10}^{2}(x)={495\over 128}\left(\sqrt{1-x^2}\right)^{2}(4199x^{8}-6188x^{6}+2730x^{4}-364x^{2}+7)$$ $$P_{10}^{3}(x)={-6435\over 16}\left(\sqrt{1-x^2}\right)^{3}(323x^{7}-357x^{5}+105x^{3}-7x)$$ $$P_{10}^{4}(x)={45045\over 16}\left(\sqrt{1-x^2}\right)^{4}(323x^{6}-255x^{4}+45x^{2}-1)$$ $$P_{10}^{5}(x)={-135135\over 8}\left(\sqrt{1-x^2}\right)^{5}(323x^{5}-170x^{3}+15x)$$ $$P_{10}^{6}(x)={675675\over 8}\left(\sqrt{1-x^2}\right)^{6}(323x^{4}-102x^{2}+3)$$ $$P_{10}^{7}(x)={-11486475\over 2}\left(\sqrt{1-x^2}\right)^{7}(19x^{3}-3x)$$ $$P_{10}^{8}(x)={34459425\over 2}\left(\sqrt{1-x^2}\right)^{8}(19x^{2}-1)$$ $$P_{10}^{9}(x)=-654729075\left(\sqrt{1-x^2}\right)^{9}x$$ $$P_{10}^{10}(x)=654729075\left(\sqrt{1-x^2}\right)^{10}$$ -->

Recurrence formula
These functions have a number of recurrence properties:

$$(\ell-m-1)(\ell-m)P_{\ell}^{m}(x) = -P_{\ell}^{m+2}(x) + P_{\ell-2}^{m+2}(x) + (\ell+m)(\ell+m-1)P_{\ell-2}^{m}(x)$$

$$(\ell-m+1)P_{\ell+1}^{m}(x) = (2\ell+1)xP_{\ell}^{m}(x) - (\ell+m)P_{\ell-1}^{m}(x)$$

$$2mxP_{\ell}^{m}(x)=-\sqrt{1-x^2}\left[P_{\ell}^{m+1}(x)+(\ell+m)(\ell-m+1)P_{\ell}^{m-1}(x)\right]$$

$$\frac{1}{\sqrt{1-x^2}}P_\ell^m(x) = \frac{-1}{2m} \left[ P_{\ell-1}^{m+1}(x) + (\ell+m-1)(\ell+m)P_{\ell-1}^{m-1}(x) \right]$$

$$\frac{1}{\sqrt{1-x^2}}P_\ell^m(x) = \frac{-1}{2m} \left[ P_{\ell+1}^{m+1}(x) + (\ell-m+1)(\ell-m+2)P_{\ell+1}^{m-1}(x) \right]$$

$$ \sqrt{1-x^2}P_\ell^m(x) = \frac1{2\ell+1} \left[ (\ell-m+1)(\ell-m+2) P_{\ell+1}^{m-1}(x) - (\ell+m-1)(\ell+m) P_{\ell-1}^{m-1}(x) \right] $$

$$ \sqrt{1-x^2}P_\ell^m(x) = \frac{-1}{2\ell+1} \left[ P_{\ell+1}^{m+1}(x) - P_{\ell-1}^{m+1}(x) \right] $$

$$\sqrt{1-x^2}P_\ell^{m+1}(x) = (\ell-m)xP_{\ell}^{m}(x) - (\ell+m)P_{\ell-1}^{m}(x)$$

$$\sqrt{1-x^2}P_\ell^{m+1}(x) = (\ell-m+1)P_{\ell+1}^m(x) - (\ell+m+1)xP_\ell^m(x)$$

$$ \sqrt{1-x^2}\frac{d}{dx}{P_\ell^m}(x) = \frac12 \left[ (\ell+m)(\ell-m+1)P_\ell^{m-1}(x) - P_\ell^{m+1}(x) \right] $$

$$ (1-x^2)\frac{d}{dx}{P_\ell^m}(x) = \frac1{2\ell+1} \left[ (\ell+1)(\ell+m)P_{\ell-1}^m(x) - \ell(\ell-m+1)P_{\ell+1}^m(x) \right] $$

$$(x^2-1)\frac{d}{dx}{P_{\ell}^{m}}(x) = {\ell}xP_{\ell}^{m}(x) - (\ell+m)P_{\ell-1}^{m}(x)$$

$$(x^2-1)\frac{d}{dx}{P_{\ell}^{m}}(x) = -(\ell+1)xP_{\ell}^{m}(x) + (\ell-m+1)P_{\ell+1}^{m}(x)$$

$$(x^2-1)\frac{d}{dx}{P_{\ell}^{m}}(x) = \sqrt{1-x^2}P_{\ell}^{m+1}(x) + mxP_{\ell}^{m}(x)$$

$$(x^2-1)\frac{d}{dx}{P_{\ell}^{m}}(x) = -(\ell+m)(\ell-m+1)\sqrt{1-x^2}P_{\ell}^{m-1}(x) - mxP_{\ell}^{m}(x)$$

Helpful identities (initial values for the first recursion):

$$P_{\ell +1}^{\ell +1}(x) = - (2\ell+1) \sqrt{1-x^2} P_{\ell}^{\ell}(x)$$ $$P_{\ell}^{\ell}(x) = (-1)^\ell (2\ell-1)!! (1- x^2)^{(\ell/2)}$$ $$P_{\ell +1}^{\ell}(x) = x (2\ell+1) P_{\ell}^{\ell}(x)$$

with $!!$ the double factorial.

Gaunt's formula
The integral over the product of three associated Legendre polynomials (with orders matching as shown below) is a necessary ingredient when developing products of Legendre polynomials into a series linear in the Legendre polynomials. For instance, this turns out to be necessary when doing atomic calculations of the Hartree–Fock variety where matrix elements of the Coulomb operator are needed. For this we have Gaunt's formula $$\begin{align} \frac{1}{2} \int_{-1}^1 P_l^u(x) P_m^v(x) P_n^w(x) dx ={}&{}(-1)^{s-m-w}\frac{(m+v)!(n+w)!(2s-2n)!s!}{(m-v)!(s-l)!(s-m)!(s-n)!(2s+1)!} \\ &{}\times \ \sum_{t=p}^q (-1)^t \frac{(l+u+t)!(m+n-u-t)!}{t!(l-u-t)!(m-n+u+t)!(n-w-t)!} \end{align}$$ This formula is to be used under the following assumptions:
 * 1) the degrees are non-negative integers $$l,m,n\ge0$$
 * 2) all three orders are non-negative integers $$u,v,w\ge 0$$
 * 3) $$u$$ is the largest of the three orders
 * 4) the orders sum up $$u=v+w$$
 * 5) the degrees obey $$ m\ge n$$

Other quantities appearing in the formula are defined as $$ 2s = l+m+n $$ $$ p = \max(0,\,n-m-u) $$ $$ q = \min(m+n-u,\,l-u,\,n-w) $$

The integral is zero unless
 * 1) the sum of degrees is even so that $$s$$ is an integer
 * 2) the triangular condition is satisfied $$m+n\ge l \ge m-n$$

Dong and Lemus (2002) generalized the derivation of this formula to integrals over a product of an arbitrary number of associated Legendre polynomials.

Generalization via hypergeometric functions
These functions may actually be defined for general complex parameters and argument:

$$P_{\lambda}^{\mu}(z) = \frac{1}{\Gamma(1-\mu)} \left[\frac{1+z}{1-z}\right]^{\mu/2} \,_2F_1 (-\lambda, \lambda+1; 1-\mu; \frac{1-z}{2})$$

where $$\Gamma$$ is the gamma function and $$ _2F_1$$ is the hypergeometric function

$$\,_2F_1 (\alpha, \beta; \gamma; z) = \frac{\Gamma(\gamma)}{\Gamma(\alpha)\Gamma(\beta)} \sum_{n=0}^\infty\frac{\Gamma(n+\alpha)\Gamma(n+\beta)}{\Gamma(n+\gamma)\ n!}z^n,$$

They are called the Legendre functions when defined in this more general way. They satisfy the same differential equation as before:

$$(1-z^2)\,y'' -2zy' + \left(\lambda[\lambda+1] - \frac{\mu^2}{1-z^2}\right)\,y = 0.\,$$

Since this is a second order differential equation, it has a second solution, $$Q_\lambda^{\mu}(z)$$, defined as:

$$Q_{\lambda}^{\mu}(z) = \frac{\sqrt{\pi}\ \Gamma(\lambda+\mu+1)}{2^{\lambda+1}\Gamma(\lambda+3/2)}\frac{1}{z^{\lambda+\mu+1}}(1-z^2)^{\mu/2} \,_2F_1 \left(\frac{\lambda+\mu+1}{2}, \frac{\lambda+\mu+2}{2}; \lambda+\frac{3}{2}; \frac{1}{z^2}\right)$$

$$P_\lambda^{\mu}(z)$$ and $$Q_\lambda^{\mu}(z)$$ both obey the various recurrence formulas given previously.

Reparameterization in terms of angles
These functions are most useful when the argument is reparameterized in terms of angles, letting $$x = \cos\theta$$:

$$P_\ell^{m}(\cos\theta) = (-1)^m (\sin \theta)^m\ \frac{d^m}{d(\cos\theta)^m}\left(P_\ell(\cos\theta)\right)$$

Using the relation $$(1 - x^2)^{1 / 2} = \sin\theta$$, the list given above yields the first few polynomials, parameterized this way, as:

$$\begin{align} P_0^0(\cos\theta) & = 1 \\[8pt] P_1^0(\cos\theta) & = \cos\theta \\[8pt] P_1^1(\cos\theta) & = -\sin\theta \\[8pt] P_2^0(\cos\theta) & = \tfrac{1}{2} (3\cos^2\theta-1) \\[8pt] P_2^1(\cos\theta) & = -3\cos\theta\sin\theta \\[8pt] P_2^2(\cos\theta) & = 3\sin^2\theta \\[8pt] P_3^0(\cos\theta) & = \tfrac{1}{2} (5\cos^3\theta-3\cos\theta) \\[8pt] P_3^1(\cos\theta) & = -\tfrac{3}{2} (5\cos^2\theta-1)\sin\theta \\[8pt] P_3^2(\cos\theta) & = 15\cos\theta\sin^2\theta \\[8pt] P_3^3(\cos\theta) & = -15\sin^3\theta \\[8pt] P_4^0(\cos\theta) & = \tfrac{1}{8} (35\cos^4\theta-30\cos^2\theta+3) \\[8pt] P_4^1(\cos\theta) & = - \tfrac{5}{2} (7\cos^3\theta-3\cos\theta)\sin\theta \\[8pt] P_4^2(\cos\theta) & = \tfrac{15}{2} (7\cos^2\theta-1)\sin^2\theta \\[8pt] P_4^3(\cos\theta) & = -105\cos\theta\sin^3\theta \\[8pt] P_4^4(\cos\theta) & = 105\sin^4\theta \end{align}$$

The orthogonality relations given above become in this formulation: for fixed m, $$P_\ell^m(\cos\theta)$$ are orthogonal, parameterized by θ over $$[0, \pi]$$, with weight $$\sin \theta$$:

$$\int_0^\pi P_k^{m}(\cos\theta) P_\ell^{m}(\cos\theta)\,\sin\theta\,d\theta = \frac{2 (\ell+m)!}{(2\ell+1)(\ell-m)!}\ \delta _{k,\ell}$$

Also, for fixed ℓ:

$$\int_0^\pi P_\ell^{m}(\cos\theta) P_\ell^{n}(\cos\theta) \csc\theta\,d\theta = \begin{cases} 0 & \text{if } m\neq n \\ \frac{(\ell+m)!}{m(\ell-m)!} & \text{if } m=n\neq0 \\ \infty & \text{if } m=n=0\end{cases}$$

In terms of θ, $$P_\ell^{m}(\cos \theta)$$ are solutions of

$$\frac{d^{2}y}{d\theta^2} + \cot \theta \frac{dy}{d\theta} + \left[\lambda - \frac{m^2}{\sin^2\theta}\right]\,y = 0\,$$

More precisely, given an integer m$$\ge$$0, the above equation has nonsingular solutions only when $$\lambda = \ell(\ell+1)\,$$ for ℓ an integer ≥ m, and those solutions are proportional to $$P_\ell^{m}(\cos \theta)$$.

Applications in physics: spherical harmonics
In many occasions in physics, associated Legendre polynomials in terms of angles occur where spherical symmetry is involved. The colatitude angle in spherical coordinates is the angle $$\theta$$ used above. The longitude angle, $$\phi$$, appears in a multiplying factor. Together, they make a set of functions called spherical harmonics. These functions express the symmetry of the two-sphere under the action of the Lie group SO(3).

What makes these functions useful is that they are central to the solution of the equation $$\nabla^2\psi + \lambda\psi = 0$$ on the surface of a sphere. In spherical coordinates θ (colatitude) and φ (longitude), the Laplacian is

$$\nabla^2\psi = \frac{\partial^2\psi}{\partial\theta^2} + \cot \theta \frac{\partial \psi}{\partial \theta} + \csc^2 \theta\frac{\partial^2\psi}{\partial\phi^2}.$$

When the partial differential equation

$$\frac{\partial^2\psi}{\partial\theta^2} + \cot \theta \frac{\partial \psi}{\partial \theta} + \csc^2 \theta\frac{\partial^2\psi}{\partial\phi^2} + \lambda \psi = 0$$

is solved by the method of separation of variables, one gets a φ-dependent part $$\sin(m\phi)$$ or $$\cos(m\phi)$$ for integer m≥0, and an equation for the θ-dependent part

$$\frac{d^{2}y}{d\theta^2} + \cot \theta \frac{dy}{d\theta} + \left[\lambda - \frac{m^2}{\sin^2\theta}\right]\,y = 0\,$$

for which the solutions are $$P_\ell^{m}(\cos \theta)$$ with $$\ell{\ge}m$$ and $$\lambda = \ell(\ell+1)$$.

Therefore, the equation

$$\nabla^2\psi + \lambda\psi = 0$$

has nonsingular separated solutions only when $$\lambda = \ell(\ell+1)$$, and those solutions are proportional to

$$P_\ell^{m}(\cos \theta)\ \cos (m\phi)\ \ \ \ 0 \le m \le \ell$$

and

$$P_\ell^{m}(\cos \theta)\ \sin (m\phi)\ \ \ \ 0 < m \le \ell.$$

For each choice of ℓ, there are 2ℓ + 1 functions for the various values of m and choices of sine and cosine. They are all orthogonal in both ℓ and m when integrated over the surface of the sphere.

The solutions are usually written in terms of complex exponentials:

$$Y_{\ell, m}(\theta, \phi) = \sqrt{\frac{(2\ell+1)(\ell-m)!}{4\pi(\ell+m)!}}\ P_\ell^{m}(\cos \theta)\ e^{im\phi}\qquad -\ell \le m \le \ell. $$ The functions $$Y_{\ell, m}(\theta, \phi)$$ are the spherical harmonics, and the quantity in the square root is a normalizing factor. Recalling the relation between the associated Legendre functions of positive and negative m, it is easily shown that the spherical harmonics satisfy the identity

$$Y_{\ell, m}^*(\theta, \phi) = (-1)^m Y_{\ell, -m}(\theta, \phi).$$

The spherical harmonic functions form a complete orthonormal set of functions in the sense of Fourier series. Workers in the fields of geodesy, geomagnetism and spectral analysis use a different phase and normalization factor than given here (see spherical harmonics).

When a 3-dimensional spherically symmetric partial differential equation is solved by the method of separation of variables in spherical coordinates, the part that remains after removal of the radial part is typically of the form

$$\nabla^2\psi(\theta, \phi) + \lambda\psi(\theta, \phi) = 0,$$

and hence the solutions are spherical harmonics.

Generalizations
The Legendre polynomials are closely related to hypergeometric series. In the form of spherical harmonics, they express the symmetry of the two-sphere under the action of the Lie group SO(3). There are many other Lie groups besides SO(3), and analogous generalizations of the Legendre polynomials exist to express the symmetries of semi-simple Lie groups and Riemannian symmetric spaces. Crudely speaking, one may define a Laplacian on symmetric spaces; the eigenfunctions of the Laplacian can be thought of as generalizations of the spherical harmonics to other settings.

Notes and references

 * ; Section 12.5. (Uses a different sign convention.)
 * ; Chapter 3.
 * ; Chapter 2.
 * Schach, S. R. (1973) New Identities for Legendre Associated Functions of Integral Order and Degree, Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, 1976, Vol. 7, No. 1 : pp. 59–69
 * ; Chapter 2.
 * Schach, S. R. (1973) New Identities for Legendre Associated Functions of Integral Order and Degree, Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, 1976, Vol. 7, No. 1 : pp. 59–69
 * Schach, S. R. (1973) New Identities for Legendre Associated Functions of Integral Order and Degree, Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, 1976, Vol. 7, No. 1 : pp. 59–69
 * Schach, S. R. (1973) New Identities for Legendre Associated Functions of Integral Order and Degree, Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, 1976, Vol. 7, No. 1 : pp. 59–69
 * Schach, S. R. (1973) New Identities for Legendre Associated Functions of Integral Order and Degree, Society for Industrial and Applied Mathematics Journal on Mathematical Analysis, 1976, Vol. 7, No. 1 : pp. 59–69

title: Associated Legendre polynomials


text:
Category:Archaeological sites

Sites of archaeological interest, where excavations or other archaeological investigations have taken place.

title: Category:Archaeological sites


text:
Patriarch Theodore II of Alexandria

Theodore (Theodoros) II (Πάπας και Πατριάρχης Αλεξανδρείας και πάσης Αφρικής Θεόδωρος Β΄; born Nikolaos Khoreftakis (Νικόλαος Χορευτάκης), November 25, 1954) is the Eastern Orthodox Patriarch of Alexandria and all Africa. He was previously a monk in the Agarathos Holy Monastery of the Assumption of the Virgin Mary.

Early life and education
He was born in the Greek island of Crete in 1954, where he completed his schooling. He is a graduate of the Rizarios Ecclesiastical School in Athens and holds a degree from the Theology Department of the Aristotle University of Thessaloniki. He also studied History of Art, Literature and Philosophy in Odesa.

He was ordained as Deacon in 1975 and Archbishop on 23 April 1978 by Metropolitan of Lambis and Sfakion Theodore Tzedakis. From 1975 to 1985, he served as Archdeacon and Chancellor of the Holy Metropolis of Lambis and Sfakion in Crete, where he developed significant Preaching and Philanthropic activities (hostels for needy youth, etc.). From 1985 to 1990 he served as Patriarchal Exarch in Russia, based in the Ukrainian city of Odesa, during the tenure of Patriarchs Nicholas VI and Parthenios.

Years of ministry
Theodore established the Institution of Hellenic Culture and the Philiki Eterea Museum with 600 children, where they were taught a thorough knowledge of Greek. In 1990, he was ordained Bishop of Kyrene and was appointed Representative of Patriarch Parthenios in Athens (1990–97). He always accompanied Patriarch Parthenios on his travels throughout Africa and to many international, interfaith and theological conferences.

In 1997, he was appointed Patriarchal Vicar of Alexandria by Patriarch Petros VII to assist him at the outset of his Patriarchate and after ten months he was elected as Metropolitan of Cameroon. He greatly developed missionary activity there. He built churches, schools and hospitals, helping many Africans and local Greeks. In 2002, he was transferred to the Holy Metropolis of Zimbabwe, where he established four missionary centres in Harare, a Hellenic Cultural Centre for 400 delegates, two large missionary centres in Malawi, with a hospital, technical schools and nursery schools. Aided by the Greek Parliament he renovated the Hellenic Square (School-Church-Vicarage) in Beira, Mozambique. He founded churches and contributed to the establishment of the Hellenic Communities of Botswana and Angola.

Patriarch of Alexandria
Following the sudden death of late Patriarch Petros in a helicopter crash, Theodore was unanimously elected on October 9, 2004 by the Synod of the Alexandrian Throne as Patriarch. The enthronement ceremony took place at the Cathedral of Annunciation in Alexandria, on Sunday, October 24, 2004, in the presence of distinguished religious and civilian representatives and a great number of faithful. He is the seventh of Patriarch of Alexandria of Cretan origin after Silvester, Meletius Pigas, Cyrillos Lucaris, Gerasimus Palladas, Gerasimus Spartaliotis and Meletius Metaxakis.

On 8 November 2019, Patriarch Theodore II formally recognised the autocephaly granted by the Ecumenical Patriarchate of Constantinople to the Orthodox Church of Ukraine earlier that year. In response, the Moscow Patriarchate (the ROC) severed eucharistic communion with Patriarch Theodore and the like-minded bishops of his church, a decision that was confirmed by the Standing Holy Synod of the ROC on 26 December 2019.

Awards

 * Order of the Holy Equal-to-the-Apostles Grand Prince Vladimir I degree (ROC, 2007)
 * Order of Glory and Honor I degree (ROC, 2013)
 * Order of the UOC-MP of the Monks Anthony and Theodosius of the Kyiv-Pechersk I degree (2007)
 * The Golden Order of St. George (Georgian Orthodox Church, 2008)
 * The Patriarch Alexy II Prize "For outstanding activities to strengthen the unity of Orthodox peoples. For the approval and promotion of Christian values in the life of society" (2012)
 * Order of the Serbian flag of the I degree (September 26, 2017, Serbia)
 * Medal of the Holy Apostle and Evangelist John the Theologian, 1st Degree (December 6, 2017, St. Petersburg Theological Academy)

title: Patriarch Theodore II of Alexandria


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Collier Street

Collier Street is a small village and civil parish in the Borough of Maidstone in Kent, England. The village is in a rural location but is close to the larger villages of Yalding, Marden and Horsmonden.

The village includes St Margaret's Church, a primary school, a small business estate and several farms. St. Margaret's church and school are at the centre of the village. The church forms part of a benefice with St. Mary's in Laddingford and St. Peter & St. Paul in Yalding. The three villages are located within three miles of each other but Collier Street, once part of Yalding's civil parish, has had its own parish since 1999. The civic or civil parish of Collier Street is governed by an elected parish council and was formed following a review by Maidstone Borough Council.

History
The village seems not to have existed before the start of the nineteenth century, nor does the road even appear on maps before the late C18th. It is most likely that the village was named for a long narrow clearing ('strait' hence 'street') through a wood used by charcoal burners (hence 'Collier'). Subsequently farms were established along with a handful of country houses before the majority of housing followed in the early Victorian era. The church was built between 1847 and 1849 and the attached school was opened in 1860.

Collier Street as a village incorporated a handful of smaller places named for the older farms or substantial houses which existed before the majority of the village's housing was built in Victorian times: for example Saxonden, Spitzbrook and Mockbeggar. A couple of old wealden roads make up the village proper; the main road which has no specific name is the B2162, part of a longer old road running from SE London / NW Kent down to Rye on the south coast.

Historically, the village was situated in the middle of a hop-growing region. Its population swelled during the harvest as whole families, often from South-East London, arrived to help bring in the hops. However, as foreign hops became cheaper and easier to source nearly all the farms moved to other arable production by the second half of the C20th. Today the fields are home to pears, strawberries and raspberries but the area is known more for its apple orchards - Collier Street has been colloquially known as 'The village in an orchard'. Some of the old hoppers' huts can still be found amongst the local orchards, fields and gardens.

Amenities
The Church of England primary school (St. Margaret's CEP) has been enlarged several times, now to accommodate more than 100 pupils. The closest comprehensive secondary school is Mascalls Academy and there are several private schools in the area. Ex-pupils of St. Margaret's typically attend Mascalls or one of the various grammar schools in the nearest towns.

The village has a population of less than 500 and is slightly unusual in having no shop, post office or pub. There were once at least two pubs in the village itself but these are now private residences: The Duke of Wellington (now Wellington House) and the Prince of Wales (now Kerry House). Two more in the parish have also closed: The Engineers (between Collier Street and Laddingford) closed in 1970 and the White Hart (Claygate) closed in 2016. There are still two pubs within a couple of miles of the village however; The Woolpack in Benover to the north and The Chequers in Laddingford to the Northwest. There was once a shop / post office at the far end of Haviker Street but this was not re-instated after a fire in 1994. There was also a shop and police station opposite Bartons Farm in the 1960s and 1970s.

Sport
Collier Street was once home to The Boarded Circuit, a Grasstrack and Longtrack motorcycle racing circuit, which held two or three events each season. The circuit was unique in being the only fully boarded permanent Grasstrack venue in the UK, but this has now closed.

title: Collier Street


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Khiam

Khiam (الخيام; sometimes spelled Khiyam) is a large town in the Nabatieh Governorate of Southern Lebanon.

Location
Khiam is situated approximately 100 km south from the capital city of Beirut and 35 km south-east from the city of Nabatieh. The border with Israel is 5 km to the south. Khiam lies at a height of 800 m above sea level.

Origin of name
E. H. Palmer wrote that the name means "The tents".

Ottoman period
In 1596, it was named as a village, Hiyam, in the Ottoman nahiya (subdistrict) of Tibnin  under the liwa' (district) of Safad, with a population of 111 households and 7 bachelors, all Muslim. The villagers paid a tax on  agricultural products, such as wheat, barley, olive trees, vineyards,  goats and beehives, in addition to "occasional revenues"; a total of 6,914 akçe.

In 1838, Eli Smith noted it as el-Khiyam; a Metawileh, "Greek" Christian and Maronite village in Merj 'Ayun.

In 1875, Victor Guérin visited: "El Khiam contains two quarters: the one on the south, with a population of 700 Metawileh, and the other on the north, with 600 Christians, divided into Maronites, Greek-Orthodox, and Greek-Catholics, with some Protestants, who have founded a chapel and a school."

In 1881, the PEF's Survey of Western Palestine (SWP) described it as: "A village, north-east of the Merj Ayun, built of stone, containing about 300 Christians and 200 Druzes. It contains a white round Moslem holy place and a modern church. It is situated on a low ridge, surrounded by figs, olives, and arable. The water supply is from three rock-cut cisterns, one birket, and the good spring of 'Ain ed Derdarah."

After independence
During the 1990s, Khiam became known for the Khiam Prison, operated by the Israeli-backed South Lebanon Army during the Israeli occupation of Southern Lebanon. Lebanese Muslim civilians were exposed to torture by Israeli and Lebanese agents in this camp and faced indefinite detention once arrested. The prison was captured by Hezbollah during the Battle of Khiam in 2000, shortly before the Israeli withdrawal from South Lebanon.

The town saw a major confrontation between the Israeli Army and Hezbollah fighters in the 2006 Lebanon War, during which a United Nations post was bombed by the Israeli Army killing four United Nations Military Observers. The IDF and Hezbollah clashed in the area once again in June 2024, with fighter jets and artillery strikes.

Notable people

 * Ali Daher (born 1996), Lebanese footballer
 * Issam Abdallah (1986-2023), Reuters video journalist

title: Khiam


text:
Mimosa (magazine)

Mimosa was a science fiction fanzine edited by Richard Lynch and Nicki Lynch. It won six Hugo Awards for Best Fanzine (in 1992, 1993, 1994, 1997, 1998 and 2003) and was nominated a total of 14 times (1991-2004). The headquarters was in Gaithersburg, Maryland.

Published from 1982 until 2003, Mimosa focused on discussions of the history and impact of science fiction fandom. Contributors included Forrest J Ackerman, Ron Bennett, John Berry, Vin¢ Clarke, Sharon N. Farber, Dave Kyle, Mike Resnick, Bob Shaw, Harry Warner, Jr., Ted White and Walt Willis.

Illustrators
The cartoonists and illustrators who contributed to Mimosa included Sheryl Birkhead, Kurt Erichsen, Debbie Hughes, Julia Morgan-Scott, Peggy Ranson, Stu Shiffman, Dan Steffan, Steve Stiles, Charlie Williams and Kip Williams. Covers by Hugo Award for Best Fan Artist winners included Brad W. Foster, Ian Gunn, Teddy Harvia and Joe Mayhew.

Issues 1-16 were produced via mimeograph, while issues 17-30 were printed commercially. The two-volume A Mimosa Fanthology collected the best from the first 27 issues.

The last article in the final issue (#30) of Mimosa (August 2003), "Footprints in the Sand" by Michael A. Burstein, is one of several articles published during the late 1990s and early 2000s pondering the possibility of science fiction fandom's eventual death.

title: Mimosa (magazine)


text:
User:Rata7

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title: User:Rata7


text:
Morgan Stewart's Coming Home

Morgan Stewart's Coming Home is a 1987 American comedy film starring Jon Cryer, Viveka Davis, Paul Gleason, Nicholas Pryor and Lynn Redgrave. The screenplay was written by Ken Hixon and David N. Titcher. The film was also released as Home Front and Homefront Riviera in some countries. The film was directed by Paul Aaron and Terry Winsor, but upon release the director was listed as "Alan Smithee", a name often used when directors ask to remove their names from a picture.

Plot
Morgan Stewart is the son of a Republican senator from Virginia who has spent most of his life away at boarding school. While disappointed he can't spend Thanksgiving with his parents, it doesn't faze him. He pulls off a major prank with three of his friends only to be busted by the Headmaster. Coincidentally, Morgan is told to he is going home when his mother calls the school and is ready for him to finally return.

Morgan is brought home to help with his father's campaign for re-election as Senator with family being the notion he sets to bring. However, Morgan's mother expects him to be conservative while his father tends to be more open to the fact that Morgan is growing up. Along the way, Morgan butts heads with both his mother and Jay, the campaign manager. Morgan decides to start doing what it takes for the family to be together, including doing chores like waxing the floors. When Morgan goes to a book signing for his idol George A. Romero, he meets fellow horror film fan Emily and the two soon begin a relationship. When Morgan "borrows" the car to go on a date with Emily, he is busted when Emily's little brother calls the police and is grounded.

Morgan soon learns that his mother has placed cameras in his room. When Morgan learns he and his father have a lot more in common than he imagined, he still faces the wrath of his mother. This comes when Emily learns that Morgan had lied about his parents but when Morgan finally loses it after losing her, he is threatened with military school by Jay. Morgan escapes using a chainsaw signed by The Texas Chain Saw Massacre's Tobe Hooper. He finally comes clean to Emily, who forgives him and the two decide to open Morgan's coin collection that his late aunt left him (after he pickpocketed Jay to get the key). They learn Jay has been embezzling campaign funds with the safety deposit box with the coin collection also containing evidence of the embezzlement. When Jay learns what has happened, he tries but ultimately fails to stop Morgan.

The end result would be Senator Stewart getting re-elected. Morgan's mother finally decides to give up her vegetarian lifestyle and eat meat. Jay serves prison time. The family butler, Ivan, becomes a real estate tycoon and leaves wife Francheska for a younger woman. Francheska returns home to Russia happily single and back on her farm with her keeping in touch with Morgan. Emily is accepted by Morgan's parents and Morgan is finally happy he has a family once again.

Production
The film was made in 1985 under the title Home Front directed by Terry Winsor. Four weeks after filming started, Winsor was fired. He was replaced by Paul Aaron but neither received credit on the film.

Film locations

 * 6th Street and Pennsylvania Avenue, SE
 * Lincoln Memorial—east side
 * Riggs Bank—Lafayette Park
 * Rock Creek Parkway
 * Washington Monument
 * White House—North Side
 * Charlottesville, Virginia—Downtown Mall & Fashion Square Mall
 * Richmond, Virginia—The University of Richmond campus
 * Miller School of Albemarle, Crozet Virginia

Soundtrack
The soundtrack included the opening track 'Painted Moon' by The Silencers and music by Peter Bernstein, Timothy Duckworth, Bernard Herrmann, Chris Isaak, John Manikoff, and The Surfaris.

Critical reception
Critics generally felt the film to be poor, although the cast, especially Jon Cryer, was usually praised. The New York Times noted that "It's hard to imagine any adult sitting through this movie without dozing off or cracking up, but it's a harmless enough fantasy, and if Jon Cryer's career takes off -- he's due in at least two more films, Dudes and Superman IV -- Morgan Stewart may find a place in the archives as an early little movie in which the star wasn't nearly matched by the material."

Rob Lowing of The Sydney Morning Herald wrote of the film "there are three good reasons to see it. However, these don't include the direction, storyline or soundtrack." She was particularly critical of the direction: "Director Smithee should cop most of the blame...a camera which wanders all over the place, a totally bland soundtrack, and fussy repetition of ideas..." Conversely, Lowing singled out actors Paul Gleason, Lynn Redgrave and Jon Cryer as the three central attractions of the film, noting that "there are flashes of brilliance, though, particularly when Cryer and Redgrave are left alone to strut their stuff."

title: Morgan Stewart's Coming Home


text:
Dominic Giampaolo

Dominic P. Giampaolo is a software developer who helped develop the Be File System for the Be Operating System (BeOS) and currently works at Apple Inc.

After graduating from Lewiston High School in Lewiston, Maine in 1987, he started studying political science at American University in Washington, D.C., but changed to computer science after one semester. After completing his bachelor's degree, he did a master's degree at Worcester Polytechnic Institute.

After graduating, he travelled to the west coast to work for Silicon Graphics in their Advanced Systems Division. There he worked in the group that ported IRIX to the 64-bit R8000 microprocessor chip set and worked on the RealityEngine and InfiniteReality graphics systems. While working for Silicon Graphics, he located and fixed a bug in Discreet Logic's Flame compositing system that was delaying post-production of the motion picture Speed.

In October 1995, Giampaolo heard about the BeBox from a friend at a poker game. Shortly after visiting the Be Inc. offices to see a demo of the computer, he began working on the BeOS, working initially in a number of areas including the kernel and the POSIX layer but most notably developing the Be File System alongside Cyril Meurillon, which replaced the Old Be File System written by Benoit Schillings which had itself replaced the original flat file system written by Meurillon. The Be File System included a number of advances compared to other personal computer filesystems in use at the time, such as a journal to improve reliability and support for extensive metadata that can be indexed to respond quickly to searches.

After Be, Giampaolo worked at Google and then QNX Software Systems. While at QNX, he discovered a bug in the Instruction Fetch Unit of Intel Pentium II and Pentium III processors.

Since March 2002, Giampaolo has been working for Apple Inc., where he is part of the macOS file system (Apple File System project) and Spotlight groups.

title: Dominic Giampaolo