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Acadiana

Acadiana (French and Louisiana French: L'Acadiane), also known as the Cajun Country (Louisiana French: Le Pays Cadjin, País Cajún), is the official name given to the French Louisiana region that has historically contained much of the state's Francophone population.

Many inhabitants of the Cajun Country have Acadian ancestry and identify as Cajuns or Creoles. Of the 64 parishes that make up the U.S. state of Louisiana, 22 named parishes and other parishes of similar cultural environment make up this intrastate region.

Etymology
The word "Acadiana" reputedly has two origins. Its first recorded appearance dates to the October 15, 1946, when a Crowley, Louisiana, newspaper, the Crowley Daily Signal, coined the term in reference to the area of Louisiana in which French descendants of the Acadians settled. However, KATC television in Lafayette independently coined "Acadiana" in the early 1960s, giving it a new, broader meaning, and popularized it throughout southern Louisiana. Founded in 1962, KATC was owned by the Acadian Television Corporation. In early 1963, the ABC affiliate received an invoice erroneously addressed to the "Acadiana" Television Corp. Someone had typed an extra "a" at the end of the word "Acadian". The station started using it to describe the region covered by its broadcast signal.

Today, numerous business, governmental, and nonprofit organizations incorporate Acadiana in their names, e.g., Mall of Acadiana and Acadiana High School. Notably, KLFY-TV, the regional CBS affiliate, used the term in its very successful "Hello News" branding campaign as "Hello Acadiana". KATC hosts a morning television show, "Good Morning Acadiana".

History
Historically part of French Louisiana, present-day Acadiana was inhabited by Attakapa Native Americans at the time of European encounter. After the expulsion of French-speaking Acadian refugees from Canada by the victorious British at the end of the Seven Years' War, many Acadians settled in this region. The Acadians intermarried with other settlers, forming what became known as Cajun culture.

In 1971, the Louisiana State Legislature officially recognized 22 Louisiana parishes and "other parishes of similar cultural environment" for their "strong French Acadian cultural aspects" (House Concurrent Resolution No. 496, June 6, 1971, authored by Carl W. Bauer of St. Mary Parish). It made "Heart of Acadiana" the official name of the region. The public, however, prefers using Acadiana to refer to the region. The official term appears on regional maps and highway markers.

Effects of hurricanes
Like much of Louisiana, this area is subject to damaging hurricanes. On October 3, 2002, the central Acadiana region suffered a direct hit from category one Hurricane Lili. The hurricane caused most of Acadiana to lose power, and some areas lost phone service. In addition, some high-rise buildings in downtown Lafayette had windows broken, and the roofs were damaged of many homes throughout the region. The high winds of Lili toppled the tower of KLFY TV-10 onto the station's studio facilities. Only one injury inside the station was reported from the tower's collapse.

The eastern Acadiana region was somewhat affected by Hurricane Katrina on August 29, 2005, although the damage was limited compared to the severe flooding farther east in Greater New Orleans. This area was used by many evacuees when they returned to the region as a "last stop" of temporary domicile before returning to Greater New Orleans. The Greater Baton Rouge area had already been handling numerous evacuees. Governor Kathleen Blanco made a public request that those returning not try to seek lodging in the capital due to this crisis of overpopulation.

Lafayette and several other municipalities set up both public and church-run shelters to handle the influx. The largest of these shelters, run by the Red Cross, was the Lafayette sports arena (the Cajundome), holding a reported 9,800 persons.

The western Acadiana region and east Texas were most affected by Hurricane Rita which hit on September 24, 2005. The Greater Lake Charles metropolitan area suffered the majority of the damage.

On Labor Day 2008, Hurricane Gustav caused severe damage to the region. Although Lafayette, Saint Martinville and Crowley had little damage (comparatively) and some residents still had power, the rest of the region was severely affected. From Alexandria to the coast and Baton Rouge to Lake Charles, massive power failures and flooding were reported. Most notable was the flooding south of Louisiana Highway 14 and the communities there. U.S. 90 was shut down for several days due to the flooding caused by Hurricane Gustav.

The total death toll from Hurricane Gustav in Acadiana was limited. This was attributed to the evacuation and mitigation plans that had been drilled by state and local official, and to a strong presence of representatives from both the Department of Homeland Security and the Federal Emergency Management Agency. In total, almost two million people along the Louisiana coast were evacuated in over two days. Gustav preparations comprised the largest evacuation in Louisiana history, and one of the most successful evacuations in the nation's history.

In 2020, Hurricane Laura caused significant damage to the western-most portion of Acadiana, including Calcasieu, Cameron, Jeff Davis, and portions of Vermilion and Acadia. A confirmed 18 people died in the storm and its aftermath. In addition, Intracoastal City saw a storm surge of 6 ft. Storm surge also flooded over SH 317 at Burns Point in St. Mary Parish, and flash flooding surrounded homes in Abbeville.

Six weeks later, Hurricane Delta made landfall near Creole, Louisiana, with winds of 100 mph. Virtually the same parishes were affected by Hurricanes Laura and Delta. Over 740,000 residents had no power following both storms.

Geography
Acadiana consists mainly of low gentle hills in the north section and dry land prairies, with marshes and bayous in the south closer to the Gulf Coast area. The wetlands increase in frequency in and around the Calcasieu River, Atchafalaya Basin, and the Mississippi River Delta. The area is cultivated with fields of rice and sugarcane.

Acadiana, as defined by the Louisiana legislature, refers to the area that stretches from just west of New Orleans to the Texas border along the Gulf of Mexico coast, and about 100 mi inland to Marksville. This includes the 22 parishes of Acadia, Ascension, Assumption, Avoyelles, Calcasieu, Cameron, Evangeline, Iberia, Iberville, Jefferson Davis, Lafayette, Lafourche, Pointe Coupee, St. Charles, St. James, St. John The Baptist, St. Landry, St. Martin, St. Mary, Terrebonne, Vermilion, and West Baton Rouge. The total land area of Acadiana is 14574.105 sqmi. If Acadiana was a U.S. state, it would be larger than Maryland; if it were a sovereign state, it would be larger than the Bahamas.

Three of the parishes (St. Charles, St. James, and St. John the Baptist) are considered the River Parishes and made up the area formerly known as the German Coast or les côtes des Allemands, because of settlement by German immigrants in the 18th century. Ascension Parish is sometimes included within the River Parishes; the River Parishes border the first and third largest regions in Louisiana by population (the Greater New Orleans area and Florida Parishes). St. James and Ascension parishes were originally known as the Comté d'Acadie (Acadia County) because of the initial settlement of 18th-century exiled Acadians. St. James Parish was known as the First Acadian Coast and Ascension Parish was known as the Second Acadian Coast. Collectively they were known as les côtes des Acadiens, the Acadian Coasts.

Major cities
The largest metropolitan areas in Acadiana are Lafayette, Lake Charles, and Houma-Thibodaux. Other cities and towns within Acadiana are Abbeville, Berwick, Breaux Bridge, Broussard, Bunkie, Carencro, Church Point, Crowley, Donaldsonville, Erath, Eunice, Franklin, Gonzales, Gueydan, Jeanerette, Jennings, Kaplan, Lutcher, Mamou, Marksville, Maurice, Morgan City, New Iberia, New Roads, Opelousas, Patterson, Plaquemine, Port Allen, Rayne, Scott, Simmesport, St. Amant, St. Gabriel, St. Martinville, Sulphur, Sunset, Ville Platte, and Youngsville.

Demographics
At the 2000 U.S. census the total population of Acadiana was 1,352,646 residents. At the 2019 American Community Survey, the tabulated population of Acadiana was an estimated 1,490,449. In 2020, the tabulated population of Acadiana's parishes was 1,486,345.

Cajun-Creole ethnicity
Cajuns are the descendants of 18th-century Acadian exiles from what are now Canada's Maritime Provinces, expelled by the British and New Englanders during and after the French and Indian War (see Expulsion of the Acadians). They prevail among the region's visible cultures, but not everyone who lives in Acadiana is ethnically Acadian or speaks Louisiana French. Similarly, not everyone who is culturally "Cajun" is descended from the Acadian refugees.

German and Polish settlers found their way to this area as early as 1721, settling an area that became known as the German Coast. They preceded the Acadians. Acadiana is home to several Native American tribes, including the Chitimacha, Houma, Tunica-Biloxi, Attakapas, and Coushatta. Acadiana also is home to other ethnic groups, including Anglo-Americans, who came into the region in increasing numbers beginning notably with the Louisiana Purchase of 1803. Since the late 20th century, political refugees from Southeast Asia (Laos, Vietnam, and Cambodia, among others) have brought their families, cultures, and languages to the area, and have contributed significantly to its fishing industry.

The region also boasts a large population of Creoles, descendants of the region's original settlers who arrived in Louisiana before and after the arrival of the Acadians. In the broadest sense, the term "Creole" has been used to denote anyone who is "native to Louisiana", regardless of race or ethnic origin. In this sense, Creoles can identify as black, white, and persons of mixed-race origin. The term has also come to denote cultural origins in addition to racial classification. While many in Acadiana associate Creoles specifically with those people descended from the gens de couleur libres (free people of color), others cling to the word's original definition, so Creoles of every ethnic background are still present in the region. Many Creoles also identify as Cajuns (and vice versa), whereas others reject association with one identity while still claiming the other. The two identities have never been mutually exclusive of one another, and documents written in Acadiana throughout the 19th century often make references to Acadiana's "Creole populations" that are understood to include people of Acadian descent.

Prior to the U.S. Civil War, Louisiana Creoles of color were a class of free people who either gained their freedom or were born into free families. The gens de couleur libres played an important role in the history of New Orleans and French Louisiana, both under French and Spanish occupation, and after the Louisiana Purchase by the United States. Some Creoles of color were wealthy businessmen, entrepreneurs, clothiers, real estate developers, doctors, and other respected professions; they owned estates and properties in French Louisiana. Being a French, and later Spanish colony, Louisiana maintained a three-tiered society that was very similar to other Latin American and Caribbean countries.

In the colonial period of French and Spanish rule, men tended to marry later after becoming financially established. Men frequently took Native American women as their wives (see Marriage à la façon du pays), and as slaves were imported into the colony, settlers also took African wives. Intermarriage between the different groups of Louisiana created a large multiracial Creole population.

As more families settled Louisiana, young Frenchmen or French Creoles coming from wealthy backgrounds courted mixed-race women as their mistresses, known as placées, before they officially married. The gens de couleur libres developed formal arrangements for placées, which the young women's mothers negotiated. Under the system of plaçage, the suitor had to be wealthy and prove that he could support the daughter, and take care of their children. Often the mothers arranged a kind of dowry or property transfer to their daughters; if the daughter was a slave, she and their children would gain freedom. The fathers often paid for the education of their mixed-race children from plaçage relationships, especially if they were sons, generally sending them to France to be educated.

Many descendants of the gens de couleur libres, or free people of color, of the Louisiana area celebrate their culture and heritage through a New Orleans-based Louisiana Creole Research Association (LA Créole). The term Créole is not synonymous with "free people of color" or gens de couleur libres, but many members of LA Créole have traced their genealogies through those lines. Today, the multiracial descendants of the French and Spanish colonists, Africans, and other ethnicities are widely known as Louisiana Creoles. Louisiana's Governor Bobby Jindal signed Act 276 on 14 June 2013, creating the license plate "I'm Creole", honoring Louisiana Creoles' contributions and heritage.

Similarly, the Acadiana region is home to many African Americans, who have contributed greatly to the region over the centuries. Many primarily descend from those persons brought to the State of Louisiana in various waves during the colonial period to work the area's sugarcane and rice plantations in the southern part of the state and the cotton plantations in the northern part of the state. Between 1723 and 1769, most slaves imported to Louisiana were from modern day Senegal, Mali and Congo, many thousands being imported to Louisiana from there. A large number of the imported slaves from the Senegambia region were members of the Wolof and Bambara ethnic groups. Saint-Louis and Goree Island were sites where a great number of slaves destined for Louisiana departed from Africa.

During the Spanish control of Louisiana, between 1770 and 1803, most of the slaves still came from the Congo and the Senegambia region, but others were imported from modern-day Benin. Many slaves imported during this period were members of the Nago people, a Yoruba subgroup. The slaves brought with them their cultural practices, languages, and religious beliefs rooted in spirit and ancestor worship, as well as Roman Catholic Christianity—all of which were key elements of Louisiana Voodoo. In addition, in the early nineteenth century, many Saint Dominicans also settled in Louisiana, both free people of color and slaves, following the Haitian Revolution on Saint-Domingue, contributing to the Voodoo tradition of the state. During the American period (1804–1820), almost half of the slaves came from the Congo. Before the American Civil War (1861–1865), African Americans comprised a significant portion of the state's population, with most being employed on sugar cane and cotton plantations (see history of slavery in Louisiana and Louisiana African American Heritage Trail).

Religion
Religiously, Acadiana differs from much of the American South because a majority of its people are Christians of the Roman Catholic tradition in contrast to the surrounding regions (e.g., Central and Northern Louisiana), which are part of the largely Protestant Bible Belt. This is largely attributed to the region's French, Spanish, and Caribbean influences. Among the Catholic population of Acadiana, the majority are served by the Roman Catholic Diocese of Lafayette in Louisiana, though some areas in western and eastern Acadiana belong to the Diocese of Lake Charles, and the Roman Catholic Diocese of Baton Rouge in the Florida Parishes.

Transportation
The traditional industries of the area, agriculture, petroleum, and tourism, initially drove the need for transportation development. In recent years, hurricane evacuation plans for the area's growing towns and cities have hastened the planning and construction of better roadways. The abundance of swamps and marshes previously made Acadiana difficult to access, a major reason for the near isolation of the early Cajun people.

After oil was found in the area in the early 20th century, oil industry development was geared to improving access by roads and waterways. Damage has been done to the region by dredging and straightening of waterways, which has damaged the wetlands that used to absorb water and storms, leaving the area more vulnerable. Coastline continues to erode.

Land
High-capacity, modern highways are the lifelines of the region. U.S. highways 90, 190, and 167 were the main connectors through south Louisiana until the 1950s. Interstates 10, 210, 55, and 49 now play the major role in transportation. US and state highways also cross the region.

Rail transport through the area is limited by the difficult terrain and the sheer number of bridges required to build over numerous streams and bayous. A robust railroad system was being built at the time of the American Civil War, but much of it was destroyed during the conflict. By the end of the war, river transport via paddlewheeler had taken over as the preferred mode of travel. The major railways in operation through the region are the Burlington Northern Santa Fe Railroad and the Union Pacific Railroad.

Water
Waterways are vital to the commercial and recreational activities of the region. Seaports, rivers, lakes, bayous, canals, and spillways dot the landscape, and served as the primary source of shipping and travel through the early 1930s. The Mississippi River is important to the eastern section, the Atchafalaya River to the middle. Calcasieu River flowing through Lake Charles enables shipping traffic in the western portion, while the Sabine River forms the western border of both Acadiana and Louisiana. Fresh and saltwater lakes, along with almost the entire Louisiana portion of the Intracoastal Waterway, enable the flow of people and materials.

Air
Airports in Lafayette and Lake Charles provide scheduled airline service. Helicopter pilots serve the oilfields in the Gulf of Mexico. Small planes are used for short trips and agricultural needs. Small general aviation airports serve communities throughout the area.

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title: Acadiana


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Lochner v. New York

Lochner v. New York, 198 U.S. 45 (1905), was a landmark decision of the U.S. Supreme Court holding that a New York State statute that prescribed maximum working hours for bakers violated the bakers' right to freedom of contract under the Fourteenth Amendment to the U.S. Constitution. The decision has been effectively overturned.

The underlying case began in 1899 when Joseph Lochner, a German immigrant who owned a bakery in Utica, New York, was charged with violating New York's Bakeshop Act of 1895. The Bakeshop Act had made it a crime for New York bakeries to employ bakers for more than 10 hours per day or 60 hours per week. He was convicted and ultimately appealed to the U.S. Supreme Court. A five-justice majority of the Supreme Court held that the law violated the Due Process Clause, stating that the law constituted an "unreasonable, unnecessary and arbitrary interference with the right and liberty of the individual to contract". Four dissenting justices rejected that view, and the dissent of Oliver Wendell Holmes Jr., in particular, became one of the most famous opinions in U.S. history.

Lochner is one of the most controversial decisions in the Supreme Court's history and gave the name to what is known as the Lochner era. During that time, the Supreme Court issued several decisions invalidating federal and state statutes that sought to regulate working conditions during the Progressive Era and the Great Depression. The period ended with West Coast Hotel Co. v. Parrish (1937), in which the Supreme Court upheld the constitutionality of minimum wage legislation enacted by Washington State.

Background
New York's Bakeshop Act of 1895 made it a crime for bakeries to employ workers for more than 10 hours per day or 60 hours per week. In 1899, New York authorities indicted Joseph Lochner on a charge of violating the Bakeshop Act by permitting an employee to work more than 60 hours in one week. Lochner was a German immigrant who owned a bakery in Utica, New York. Unlike other bakeries, which used two separate shifts for evening and morning work, Lochner's bakery employed only a single crew of bakers. His bakers would arrive in the evening and prepare the bread dough, sleep for several hours in an on-site dormitory, then wake up in the early morning and bake the loaves of bread. Lochner counted his bakers' time spent sleeping in the dormitory as working hours and paid them accordingly.

Lochner's lawyer argued at his trial that the right to contract freely to be one of the rights encompassed by substantive due process. Lochner's case was argued by Henry Weismann, who had been one of the foremost advocates of the Bakeshop Act when he was Secretary of the Journeymen Bakers' Union. In his brief, Weismann decried the idea that "the treasured freedom of the individual... should be swept away under the guise of the police power of the State." He denied New York's argument that the Bakeshop Act was a necessary health measure by claiming that the "average bakery of the present day is well ventilated, comfortable both summer and winter, and always sweet smelling." Weismann's brief contained an appendix providing statistics showing that bakers' mortality rates were comparable to that of white-collar professionals.

Weismann's arguments were unsuccessful. The trial court found Lochner guilty and fined him $50. Lochner appealed to the New York Supreme Court, Appellate Division, which affirmed his conviction, then appealed to the New York Court of Appeals, which also affirmed it. He then appealed to the U.S. Supreme Court.

Supreme Court decision
On April 17, 1905, the Supreme Court issued a 5–4 decision in favor of Lochner that struck down the New York Bakeshop Act's limits on bakers' working hours as unconstitutional.

Opinion of the Court
Five justices formed the majority and joined an opinion written by Justice Rufus Peckham.

The Court began with the question of whether the Fourteenth Amendment's protections applied to freedom of contract. Citing its 1897 decision Allgeyer v. Louisiana, in which it had struck down a Louisiana law that banned buying shipping insurance from companies in other states on grounds that it violated the freedom to make contracts to carry out a trade or profession, the Court held that freedom of contract was a basic right covered by the protections for "life, liberty, and property" in the Fourteenth Amendment's Due Process Clause. "The general right to make a contract in relation to his business is part of the liberty of the individual protected by the Fourteenth Amendment to the Federal Constitution. Under that provision, no State can deprive any person of life, liberty or property without due process of law. The right to purchase or to sell labor is part of the liberty protected by this amendment unless there are circumstances which exclude the right." The Court explained that by "circumstances which exclude the right", it meant when states passed laws under the "police power"—the inherent authority of U.S. state governments to pass laws governing "health, safety, and morals". The Court said that because the Due Process Clause protected freedom of contract, state laws could only interfere with it if they were valid exercises of the police power. To guarantee this freedom, the Court said that American courts had to scrutinize state laws regulating economic freedom, such as New York's bakery law, to ensure they served valid police-power purposes.

Applying these legal principles to the facts of the case, the Court first determined that bakers' jobs were not dangerous enough to need special government protection. The Court distinguished New York's law for bakers from a Utah law for miners the Court had upheld against a Due Process challenge in its 1898 decision Holden v. Hardy, saying that, unlike mining, baking was not an unusually dangerous activity. The Court also determined that the Bakeshop Act had no relation to public health. Reasoning that the New York Legislature could not rationally have enacted the law for health reasons, the Court concluded that the Act was really a "labor law" that could not be justified under the police power. "Clean and wholesome bread does not depend upon whether the baker works but ten hours per day or only sixty hours a week. ... The [Bakeshop] act is not, within any fair meaning of the term, a health law, but is an illegal interference with the rights of individuals, both employers and employees, to make contracts regarding labor upon such terms as they may think best, or which they may agree upon with the other parties to such contracts." The Court concluded that New York had failed to prove that the Bakeshop Act's maximum-hours provision had any close connection to public health. It said that if it were to conclude otherwise, states would have unlimited power over citizens' lives. "It is also urged ... that it is to the interest of the State that its population should be strong and robust, and therefore any legislation which may be said to tend to make people healthy must be valid as health laws, enacted under the police power. ... Scarcely any law but might find shelter under such assumptions, and conduct, properly so called, as well as contract, would come under the restrictive sway of the legislature. Not only the hours of employees, but the hours of employers, could be regulated, and doctors, lawyers, scientists, all professional men, as well as athletes and artisans, could be forbidden to fatigue their brains and bodies by prolonged hours of exercise, lest the fighting strength of the State be impaired." Lastly, the Court said that state laws ostensibly enacted for police-power purposes were often really intended to redistribute wealth or help a certain group at the expense of others. "It is impossible for us to shut our eyes to the fact that many laws of this character, while passed under what is claimed to be the police power for the purpose of protecting the public health or welfare, are, in reality, passed for other motives." Having determined that Bakeshop Act had no relation to public health and that the baking profession was not unusually dangerous, the Court concluded that "the limit of the police power has been reached and passed in this case", and it struck down the act as a violation of the Fourteenth Amendment's Due Process Clause.

Harlan
Justice John Marshall Harlan wrote a dissenting opinion that was joined by Justices Edward Douglass White and William R. Day.

Harlan contended that the liberty to contract is subject to regulation imposed by a state acting within the scope of its police powers. He offered the following rule for determining whether such statutes are unconstitutional:

"The power of the courts to review legislative action in respect of a matter affecting the general welfare exists only 'when that which the legislature has done comes within the rule that, if a statute purporting to have been enacted to protect the public health, the public morals or the public safety, has no real or substantial relation to those objects, or is, beyond all question, a plain, palpable invasion of rights secured by the fundamental law.'"

Harlan asserted that the burden of proof should rest with the party seeking to have such a statute deemed unconstitutional.

Harlan argued that the Court gave insufficient weight to the state's argument that the law was a valid health measure addressing a legitimate state interest. He contended that it was "plain that this statute was enacted to protect the physical well-being of those who work in bakery and confectionery establishments." Responding to the majority's assertion that the profession of a baker was not an unhealthy one, he quoted at length from academic studies describing the respiratory ailments and other risks that bakers faced. He argued that the Supreme Court should have deferred to the New York Legislature's judgment that long working hours threatened the health of bakery employees: "If the end which the legislature seeks to accomplish be one to which its power extends, and if the means employed to that end, although not the wisest or best, are yet not plainly and palpably unauthorized by law, then the court cannot interfere."

Holmes
Justice Oliver Wendell Holmes Jr. also dissented from the Court's decision, and his three-paragraph dissent has become one of the most famous in U.S. Supreme Court history. Holmes began by accusing the majority of deciding Lochner's case by following laissez-faire economics rather than legal principles. "This case is decided upon an economic theory which a large part of the country does not entertain. If it were a question whether I agreed with that theory, I should desire to study it further and long before making up my mind. But I do not conceive that to be my duty, because I strongly believe that my agreement or disagreement has nothing to do with the right of a majority to embody their opinions in law. ... [A] Constitution is not intended to embody a particular economic theory, whether of paternalism and the organic relation of the citizen to the state or of laissez faire. It is made for people of fundamentally differing views ...."

Holmes pointed out that there were many American laws restricting citizens' freedom of contract that had never been found unconstitutional. As "ancient examples", Holmes pointed to usury laws, which set maximum interest rates for loans of money, and Sunday laws, which outlawed certain economic activities on Sundays to promote Christian observance of the Sabbath. Holmes analogized the majority's interpretation of the Fourteenth Amendment to the writings of Herbert Spencer, the 19th-century British sociologist who coined the term "survival of the fittest" and whose ideas later became associated with social Darwinism.

"The liberty of the citizen to do as he likes so long as he does not interfere with the liberty of others to do the same, which has been a shibboleth for some well known writers, is interfered with by school laws, by the Post Office, by every state or municipal institution which takes his money for purposes thought desirable, whether he likes it or not. The Fourteenth Amendment does not enact Mr. Herbert Spencer's Social Statics."

Holmes wrote that, in his view, a duly enacted state law could only be unconstitutional under the Due Process Clause's guarantee of liberty if it could rationally be said to "infringe fundamental principles" in the American tradition, and he maintained that the Bakeshop Act clearly did not do so. "Every opinion tends to become a law. I think that the word liberty in the Fourteenth Amendment is perverted when it is held to prevent the natural outcome of a dominant opinion, unless it can be said that a rational and fair man necessarily would admit that the statute proposed would infringe fundamental principles as they have been understood by the traditions of our people and our law. It does not need research to show that no such sweeping condemnation can be passed upon the statute before us."

Significance and legacy
The Supreme Court's due process jurisprudence over the next three decades was inconsistent, but it took a narrow view of states' police powers in several major labor cases after Lochner. For example, in Coppage v. Kansas (1915), the Court struck down statutes forbidding "yellow-dog contracts." Similarly, in Adkins v. Children's Hospital (1923), the Supreme Court held that minimum wage laws violated the due process clause, but Chief Justice William Howard Taft strongly dissented and suggested that the Court instead should have overruled Lochner. The doctrine of substantive due process was coupled with a narrow interpretation of congressional power under the commerce clause. Justices James McReynolds, George Sutherland, Willis Van Devanter, and Pierce Butler emerged during the 1920s and the 1930s as the foremost defenders of traditional limitations on government power on the Supreme Court and so were collectively dubbed by supporters of the New Deal the "Four Horsemen of Reaction." All four of them believed in laissez-faire economics.

In 1934, the Supreme Court decided in Nebbia v. New York that there is no constitutional fundamental right to freedom of contract. In 1937, the Supreme Court decided West Coast Hotel Co. v. Parrish, which expressly overruled Adkins and implicitly signaled the end of the Lochner era by repudiating the idea that freedom of contract should be unrestricted.

Although the Supreme Court did not explicitly overrule Lochner, it agreed to give more deference to the decisions of state legislatures. The Supreme Court sounded the death knell for economic substantive due process several years later in Williamson v. Lee Optical of Oklahoma (1955) by unanimously declaring, "The day is gone when this Court uses the Due Process Clause of the Fourteenth Amendment to strike down state laws, regulatory of business and industrial conditions, because they may be unwise, improvident, or out of harmony with a particular school of thought."

Modern substantive due process
Since the end of the Lochner era, the Supreme Court has applied a lower standard of review to confront restrictions on economic liberty. A higher standard is used in reviewing legislation infringing on personal liberties. A line of cases dating back to the 1923 opinion by Justice McReynolds in Meyer v. Nebraska, which cited Lochner as establishing limits on the police power, has established a privacy right under substantive due process. More recently, in Roe v. Wade (1973), the Supreme Court held that women have a privacy right to determine whether or not to have an abortion. In Planned Parenthood v. Casey (1992), the Supreme Court reaffirmed that right but no longer used the term "privacy" to describe it. The abortion right was later overruled in Dobbs v. Jackson Women's Health Organization (2022).

Scholarly reaction
The Supreme Court's decision in Lochner v. New York has been criticized by legal scholars. The law professor Bernard Siegan described it as "one of the most condemned cases in United States history." According to the Center for American Progress, a left-leaning thinktank, law professors often use Lochner, along with Plessy v. Ferguson and Korematsu v. United States, as examples of "how judges should not behave."

Lochner is sometimes used as shorthand for extreme right-wing constitutional theory. However, it has come under harsh criticism from conservative and libertarian jurists as well because Lochner embraced substantive due process, a doctrine that was arguably at odds with the original understanding of the Constitution. For example, the conservative legal scholar Robert Bork called the decision an "abomination" and the "quintessence of judicial usurpation of power." Similarly, former Attorney General Edwin Meese said that the Supreme Court "ignored the limitations of the Constitution and blatantly usurped legislative authority." Siegan, a self-described libertarian, described it as "a symbol of judicial dereliction and abuse."

Scholars have noted that when the Fourteenth Amendment was adopted in 1868, 27 of the 37 state constitutions had adopted references to Locke's labor theory of property, which typically said: "All men are by nature free and independent, and have certain inalienable rights, among which are those of enjoying and defending life and liberty, acquiring and possessing and protecting property: and pursuing and obtaining safety and happiness." As such clauses were "deeply rooted in American history and tradition," they likely informed the original meaning of the scope and nature of the fundamental rights protected by the Fourteenth Amendment in the eyes of Lochner-era justices.

However, the decision also has attracted libertarian defenders: the Cato Institute and the scholars Richard Epstein and Randy Barnett, who argue that it correctly protected economic liberty.

Barnett has argued that the decision was basically correct in its presumption in favor of liberty of contract and that the decision was wrong only by perpetuating the misinterpretation of the Fourteenth Amendment that had been established in the Slaughter-House Cases. According to Barnett, the liberty of contract is properly found in the Privileges or Immunities Clause, not in the Due Process Clause of the Fourteenth Amendment. David Bernstein, in Rehabilitating Lochner: Defending Individual Rights Against Progressive Reform, has argued that Lochner was well grounded in Supreme Court precedent and that its emphasis on limits to the states' police powers informed the Supreme Court's early civil liberties and civil rights cases.

title: Lochner v. New York


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Gutzon Borglum

John Gutzon de la Mothe Borglum (March 25, 1867 – March 6, 1941) was an American sculptor best known for his work on Mount Rushmore. He is also associated with various other public works of art across the U.S., including Stone Mountain in Georgia, statues of Union General Philip Sheridan in Washington D.C. and in Chicago, as well as a bust of Abraham Lincoln exhibited in the White House by Theodore Roosevelt and now held in the United States Capitol crypt in Washington, D.C.

Early life
The son of Danish immigrants, John Gutzon de la Mothe Borglum was born in 1867 in St. Charles, in what was then thought to be in Utah but was later determined to be in Idaho Territory. Borglum was a child of Mormon polygamy. His father, Jens Møller Haugaard Børglum (1839–1909), came from the village of Børglum in northwestern Denmark. He had two wives when he lived in Idaho: Gutzon's mother, Christina Mikkelsen Børglum (1847–1871), and her sister Ida, who was Jens's first wife. Jens Borglum decided to leave the LDS church and moved to Omaha, Nebraska where polygamy was both illegal and taboo. Jens Borglum had worked mainly as a woodcarver before his decision to attend the Saint Louis Homeopathic Medical College in St. Louis, Missouri. At this point "Jens and Christina divorced, the family left the LDS church, and Jens, Ida, their children, and Christina's two sons, Gutzon and Solon, moved to St. Louis, where Jens earned a medical degree." Upon his graduation from the Missouri Medical College in 1874, Dr. Borglum moved the family to Fremont, Nebraska, where he established a medical practice. Gutzon Borglum remained in Fremont until 1882, when his father enrolled him in St. Mary's College, Kansas.

After a brief stint at Saint Mary's College, Gutzon Borglum moved to Omaha, Nebraska, where he apprenticed in a machine shop and graduated from Creighton Preparatory School.

New York City
Back in the U.S. in New York City, he sculpted saints and apostles for the new Cathedral of St. John the Divine in 1901; in 1906 he had a group sculpture accepted by the Metropolitan Museum of Art — the first sculpture by a living American the museum had ever purchased—and made his presence further felt with some portraits. He also won the Logan Medal of the Arts. His reputation soon surpassed that of his younger brother Solon Borglum, already an established sculptor.

Family
In 1889, Borglum married his painting instructor, Elizabeth Jaynes Putnam, who was 18 years his senior. After divorcing his first wife, Borglum married Mary Montgomery Williams, on May 20, 1909, with whom he had three children, including a son, Lincoln, and a daughter, Mary Ellis (Mel) Borglum Vhay.

Public life
Borglum was active in the committee that organized the New York Armory Show of 1913, the birthplace of modernism in American art. By the time the show was ready to open, however, Borglum had resigned from the committee, feeling that the emphasis on avant-garde works had co-opted the original premise of the show and made traditional artists like himself look provincial. He moved into an estate in Stamford, Connecticut in 1914 and lived there for 10 years. He sheltered Czechoslovak Legion members on his land at Stamford in 1917.

Borglum was an active member of the Ancient Free and Accepted Masons (the Freemasons), raised in Howard Lodge #35, New York City, on June 10, 1904, and serving as its Worshipful Master 1910–11. In 1915, he was appointed Grand Representative of the Grand Lodge of Denmark near the Grand Lodge of New York. He received his Scottish Rite Degrees in the New York City Consistory on October 25, 1907. He was friends with Theodore Roosevelt for many years and during the 1912 United States presidential election Borglum was a very active campaign organizer and member of the Bull Moose Party.

While it has been claimed that Borglum was a member of the Ku Klux Klan, an article in the Smithsonian Magazine denies that there is proof that he officially joined the KKK. That said, he became "deeply involved in Klan politics", attending Klan rallies and serving on Klan committees. In 1925, having only completed the head of Robert E. Lee, Borglum was dismissed from the Stone Mountain project, with some holding that it came about due to infighting within the KKK, with Borglum involved in the strife. Later, he stated "I am not a member of the Kloncilium, nor a knight of the KKK," but Howard Shaff and Audrey Karl Shaff claim that "that was for public consumption." The museum at Mount Rushmore displays a letter to Borglum from D. C. Stephenson, the infamous Klan Grand Dragon who later was convicted of the rape and murder of Madge Oberholtzer. The 8x10 foot portrait contains the inscription "To my good friend Gutzon Borglum, with the greatest respect." Correspondence from Borglum to Stephenson during the 1920s detailed a deep racist conviction in Nordic moral superiority and strict immigration policies.

Monuments
A fascination with gigantic scale and themes of heroic nationalism suited his extroverted personality. His head of Abraham Lincoln, carved from a six-ton block of marble, was exhibited in Theodore Roosevelt's White House and can be found in the United States Capitol Crypt in Washington, D.C. A "patriot," believing that the "monuments we have built are not our own," he looked to create art that was "American, drawn from American sources, memorializing American achievement," according to a 1908 interview. Borglum was highly suited to the competitive environment surrounding the contracts for public buildings and monuments, and his public sculptures are found all around the United States.

In 1908, Borglum won a competition for an equestrian statue of the Civil War General Philip Sheridan to be placed in Sheridan Circle in Washington, D.C. A second version of General Philip Sheridan was erected in Chicago, Illinois, in 1923. Winning this competition was a personal triumph for him because he won out over sculptor J.Q.A. Ward, a much older and more established artist and one whom Borglum had clashed with earlier in regard to the National Sculpture Society. At the unveiling of the Sheridan statue, one observer, President Theodore Roosevelt (whom Borglum was later to include in the Mount Rushmore portrait group), declared that it was "first rate"; a critic wrote that "as a sculptor Gutzon Borglum was no longer a rumor, he was a fact." (Smith:see References)

President Franklin D. Roosevelt delivered an address on May 3, 1934, dedicating a statue of William Jennings Bryan created by Borglum. This Bryan statue by Borglum originally stood in Washington, D.C. but was later displaced by highway construction and moved by an Act of Congress in 1961 to Salem, Illinois, Bryan's birthplace.

In 1925, the sculptor moved to Texas to work on the monument to trail drivers commissioned by the Trail Drivers Association. He completed the model in 1925, but due to lack of funds it was not cast until 1940, and then was only a fourth its originally planned size. It stands in front of the Texas Pioneer and Trail Drivers Memorial Hall next to the Witte Museum in San Antonio. Borglum lived at the historic Menger Hotel, which in the 1920s was the residence of a number of artists. He subsequently planned the redevelopment of the Corpus Christi waterfront; the plan failed, although a model for a statue of Christ intended for it was later modified by his son and erected on a mountaintop in South Dakota. While living and working in Texas, Borglum took an interest in local beautification. He promoted change and modernity, although he was berated by academicians.

Stone Mountain

Borglum was initially involved in the carving of Stone Mountain in Georgia. Borglum's nativist stances made him seem an ideologically sympathetic choice to carve a memorial to heroes of the Confederate States of America, planned for Stone Mountain, Georgia. In 1915, coinciding with the Klan-glorifying, highly successful The Birth of a Nation, he was approached by the United Daughters of the Confederacy with a project for sculpting a 20 ft high bust of General Robert E. Lee on the mountain's 800 ft rockface. Borglum accepted, but told the committee, "Ladies, a twenty-foot head of Lee on that mountainside would look like a postage stamp on a barn door."

Borglum's ideas eventually evolved into a high relief frieze of Lee, Jefferson Davis, and Stonewall Jackson riding around the mountain, followed by a legion of artillery troops. Borglum agreed to include a Ku Klux Klan altar in his plans for the memorial to acknowledge a request of Helen Plane in 1915, who wrote to him: "I feel it is due to the KKK that saved us from Negro domination and carpetbag rule, that it be immortalized on Stone Mountain".

After a delay caused by World War I, Borglum and the newly chartered Stone Mountain Confederate Monumental Association set to work on this monument, the largest ever attempted. Many difficulties slowed progress, some because of the sheer scale involved. After finishing the detailed model of the carving, Borglum was unable to trace the figures onto the massive area on which he was working, until he developed a gigantic magic lantern to project the image onto the side of the mountain.

Carving officially began on June 23, 1923, with Borglum making the first cut. At Stone Mountain he developed sympathetic connections with the reorganized Ku Klux Klan, who were major financial backers of the monument. Lee's head was unveiled on Lee's birthday January 19, 1924, to a large crowd, but soon thereafter Borglum was increasingly at odds with the officials of the organization. His domineering, perfectionist, authoritarian manner brought tensions to such a point that in March 1925 Borglum smashed his clay and plaster models. He left Georgia permanently, his tenure with the organization over. None of his work remains, as it was all blasted off the mountain's face for the work of Borglum's replacement Henry Augustus Lukeman. In his abortive attempt, however, Borglum had developed the necessary techniques for sculpting on a gigantic scale that made Mount Rushmore possible.

Mount Rushmore
His Mount Rushmore project, 1927–1941, was the brainchild of South Dakota state historian Doane Robinson. His first attempt with the face of Thomas Jefferson had to be redone when it was determined that there was not enough stone to complete it. Dynamite was used to remove large areas of rock from under Washington's brow. The initial pair of presidents, George Washington and Thomas Jefferson, was soon joined by Abraham Lincoln and Theodore Roosevelt.

Ivan Houser, father of John Sherrill Houser, was assistant sculptor to Gutzon Borglum in the early years of carving; he began working with Borglum shortly after the inception of the monument and was with Borglum for a total of seven years. When Houser left Gutzon to devote his talents to his own work, Gutzon's son, Lincoln, took over as Assistant-Sculptor to his father.

Borglum alternated exhausting on-site supervising with world tours, raising money, polishing his personal legend, sculpting a Thomas Paine memorial for Paris and a Woodrow Wilson memorial for Poznań, Poland (1931). In his absence, work at Mount Rushmore was overseen by Bill Tallman and later his son, Lincoln Borglum. During the Rushmore project, father and son were residents of Beeville, Texas. When he died in Chicago, following complications of surgery, his son finished another season at Rushmore, but left the monument largely in the state of completion it had reached under his father's direction.

Other works

In 1909, the sculpture Rabboni was created as a grave site for the Ffoulke Family in Washington, D.C. at Rock Creek Cemetery.

Four public works by Borglum are in Newark, New Jersey: Seated Lincoln (1911), Indian and the Puritan (1916), Wars of America (1926), and a stele with bas-relief, First Landing Party of the Founders of Newark (1916). No other U.S. city holds as many public displays by Borglum.

In 1912, the Nathaniel Wheeler Memorial Fountain was dedicated in Bridgeport, Connecticut.

Memorial to Robert Louis Stevenson at Baker Cottage, Saranac Lake, New York. Unveiled in 1915.

In 1918, he was one of the drafters of the Czechoslovak declaration of independence.

One of Borglum's more unusual pieces is the Aviator completed in 1919 as a memorial for James Rogers McConnell, who was killed in World War I while flying for the Lafayette Escadrille. It is located on the grounds of the University of Virginia in Charlottesville, Virginia.

In 1922, he crafted the William Dempster Hoard Sculpture in the north end what is now the Henry Mall Historic District at the University of Wisconsin-Madison.

His statue of Collis P. Huntington was completed in 1924 and stands at the entrance of the CSX Huntington headquarters building located in the 900 block of Seventh Avenue Huntington, West Virginia.

His statue of Harvey W. Scott was completed in 1933 and stood at the peak of Mount Tabor, Portland, Oregon until it was toppled by protestors in 2020.

Borglum sculpted the Memorial to the "Start Westward of the United States", which is located in Muskingum Park, Marietta, Ohio (1938). The work was featured on a 1938 3¢ US postage stamp.

He built the statue of Daniel Butterfield at Sakura Park in Manhattan (1918).

He created a memorial to Sacco and Vanzetti (1928), a plaster cast of which is now in the Boston Public Library.

Another Borglum design is the North Carolina Monument on Seminary Ridge at the Gettysburg Battlefield in south-central Pennsylvania. The cast bronze sculpture depicts a wounded Confederate officer encouraging his men to push forward during Pickett's Charge. Borglum had also made arrangements for an airplane to fly over the monument during the dedication ceremony on July 3, 1929. During the sculpture's unveiling, the plane scattered roses across the field as a salute to those North Carolinians who had fought and died at Gettysburg.

In 1939 when German troops marched into Poland, they destroyed Borglum's statue of Woodrow Wilson located in Poznań.

Death
Borglum died in 1941 of a heart attack and is interred at Forest Lawn Memorial Park in Glendale, California.

In popular culture

 * Historian Simon Schama, in his Landscape and Memory, discusses Borglum's life and work.

title: Gutzon Borglum


text:
Generalized hypergeometric function

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then  be defined over a wider domain of the argument by analytic continuation. The generalized hypergeometric series is sometimes just called the hypergeometric series, though this term also sometimes just refers to the Gaussian hypergeometric series. Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials.

Notation
A hypergeometric series is formally defined as a power series
 * $$\beta_0 + \beta_1 z + \beta_2 z^2 + \dots = \sum_{n \geqslant 0} \beta_n z^n$$

in which the ratio of successive coefficients is a rational function of n. That is,
 * $$\frac{\beta_{n+1}}{\beta_n} = \frac{A(n)}{B(n)}$$

where A(n) and B(n) are polynomials in n.

For example, in the case of the series for the exponential function,
 * $$1+\frac{z}{1!}+\frac{z^2}{2!}+\frac{z^3}{3!}+\cdots,$$

we have:
 * $$ \beta_n = \frac{1}{n!}, \qquad \frac{\beta_{n+1}}{\beta_n} = \frac{1}{n+1}.$$

So this satisfies the definition with $A(n) = 1$ and $B(n) = n + 1$.

It is customary to factor out the leading term, so β0 is assumed to be 1. The polynomials can be factored into linear factors of the form (aj + n) and (bk + n) respectively, where the aj and bk are complex numbers.

For historical reasons, it is assumed that (1 + n) is a factor of B. If this is not already the case then both A and B can be multiplied by this factor; the factor cancels so the terms are unchanged and there is no loss of generality.

The ratio between consecutive coefficients now has the form
 * $$\frac{c(a_1+n)\cdots(a_p+n)}{d(b_1+n)\cdots(b_q+n)(1+n)}$$,

where c and d are the leading coefficients of A and B. The series then has the form
 * $$1 + \frac{a_1\cdots a_p}{b_1\cdots b_q \cdot 1}\frac{cz}{d} + \frac{a_1\cdots a_p}{b_1\cdots b_q \cdot 1} \frac{(a_1+1)\cdots(a_p+1)}{(b_1+1)\cdots (b_q+1) \cdot 2}\left(\frac{cz}{d}\right)^2+\cdots$$,

or, by scaling z by the appropriate factor and rearranging,
 * $$1 + \frac{a_1\cdots a_p}{b_1\cdots b_q}\frac{z}{1!} + \frac{a_1(a_1+1)\cdots a_p(a_p+1)}{b_1(b_1+1)\cdots b_q(b_q+1)}\frac{z^2}{2!}+\cdots$$.

This has the form of an exponential generating function. This series is usually denoted by
 * $${}_pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z)$$

or

 * $$\,{}_pF_q \left[\begin{matrix} a_1 & a_2 & \cdots & a_{p} \\ b_1 & b_2 & \cdots & b_q \end{matrix} ; z \right].$$

Using the rising factorial or Pochhammer symbol

 * $$\begin{align}

(a)_0 &= 1, \\ (a)_n &= a(a+1)(a+2) \cdots (a+n-1), && n \geq 1 \end{align}$$

this can be written

 * $$\,{}_pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(b_1)_n\cdots(b_q)_n} \, \frac {z^n} {n!}.$$

(Note that this use of the Pochhammer symbol is not standard; however it is the standard usage in this context.)

Terminology
When all the terms of the series are defined and it has a non-zero radius of convergence, then the series defines an analytic function. Such a function, and its analytic continuations, is called the hypergeometric function.

The case when the radius of convergence is 0 yields many interesting series in mathematics, for example the incomplete gamma function has the asymptotic expansion
 * $$\Gamma(a,z) \sim z^{a-1}e^{-z}\left(1+\frac{a-1}{z}+\frac{(a-1)(a-2)}{z^2} + \cdots\right)$$

which could be written za−1e−z 2F0(1−a,1;;−z−1). However, the use of the term hypergeometric series is usually restricted to the case where the series defines an actual analytic function.

The ordinary hypergeometric series should not be confused with the basic hypergeometric series, which, despite its name, is a rather more complicated and recondite series. The "basic" series is the q-analog of the ordinary hypergeometric series. There are several such generalizations of the ordinary hypergeometric series, including the ones coming from zonal spherical functions on Riemannian symmetric spaces.

The series without the factor of n! in the denominator (summed over all integers n, including negative) is called the bilateral hypergeometric series.

Convergence conditions
There are certain values of the aj and bk for which the numerator or the denominator of the coefficients is 0.
 * If any aj is a non-positive integer (0, −1, −2, etc.) then the series only has a finite number of terms and is, in fact, a polynomial of degree −aj.
 * If any bk is a non-positive integer (excepting the previous case with bk < aj) then the denominators become 0 and the series is undefined.

Excluding these cases, the ratio test can be applied to determine the radius of convergence.
 * If p < q + 1 then the ratio of coefficients tends to zero. This implies that the series converges for any finite value of z and thus defines an entire function of z. An example is the power series for the exponential function.
 * If p = q + 1 then the ratio of coefficients tends to one. This implies that the series converges for |z| < 1 and diverges for |z| > 1. Whether it converges for |z| = 1 is more difficult to determine. Analytic continuation can be employed for larger values of z.
 * If p > q + 1 then the ratio of coefficients grows without bound. This implies that, besides z = 0, the series diverges. This is then a divergent or asymptotic series, or it can be interpreted as a symbolic shorthand for a differential equation that the sum satisfies formally.

The question of convergence for p=q+1 when z is on the unit circle is more difficult. It can be shown that the series converges absolutely at z = 1 if
 * $$\Re\left(\sum b_k - \sum a_j\right)>0$$.

Further, if p=q+1, $$\sum_{i=1}^{p}a_{i}\geq\sum_{j=1}^{q}b_{j}$$ and z is real, then the following convergence result holds :
 * $$\lim_{z\rightarrow 1}(1-z)\frac{d\log(_{p}F_{q}(a_{1},\ldots,a_{p};b_{1},\ldots,b_{q};z^{p}))}{dz}=\sum_{i=1}^{p}a_{i}-\sum_{j=1}^{q}b_{j}$$.

Basic properties
It is immediate from the definition that the order of the parameters aj, or the order of the parameters bk can be changed without changing the value of the function. Also, if any of the parameters aj is equal to any of the parameters bk, then the matching parameters can be "cancelled out", with certain exceptions when the parameters are non-positive integers. For example,
 * $$\,{}_2F_1(3,1;1;z) = \,{}_2F_1(1,3;1;z) = \,{}_1F_0(3;;z)$$.

This cancelling is a special case of a reduction formula that may be applied whenever a parameter on the top row differs from one on the bottom row by a non-negative integer.

{}_{A+1}F_{B+1}\left[ \begin{array}{c} a_{1},\ldots ,a_{A},c + n \\ b_{1},\ldots ,b_{B},c \end{array} \begin{array}{c} a_{1} + j,\ldots ,a_{A} + j \\ b_{1} + j,\ldots ,b_{B} + j \end{array} $$
 * z\right] = \sum_{j = 0}^n \binom{n}{j} \frac{z^j}{(c)_j} \frac{\prod_{i = 1}^A (a_i)_j}{\prod_{i = 1}^B (b_i)_j} {}_AF_B\left[
 * z\right]

Euler's integral transform
The following basic identity is very useful as it relates the higher-order hypergeometric functions in terms of integrals over the lower order ones

 * $$ {}_{A+1}F_{B+1}\left[

\begin{array}{c} a_{1},\ldots ,a_{A},c \\ b_{1},\ldots ,b_{B},d \end{array} \int_{0}^{1}t^{c-1}(1-t)_ – ^{d-c-1}\ {}_{A}F_{B}\left[ \begin{array}{c} a_{1},\ldots ,a_{A} \\ b_{1},\ldots ,b_{B} \end{array} ; tz\right] dt$$
 * z\right] =\frac{\Gamma (d)}{\Gamma (c)\Gamma (d-c)}

Differentiation
The generalized hypergeometric function satisfies
 * $$\begin{align}

\left (z\frac{{\rm{d}}z} + a_j \right ){}_pF_q\left[ \begin{array}{c} a_1,\dots,a_j,\dots,a_p \\ b_1,\dots,b_q\end{array} ;z\right] &= a_j \; {}_pF_q\left[ \begin{array}{c} a_1,\dots,a_j+1,\dots,a_p \\ b_1,\dots,b_q \end{array} ;z\right] \\ \end{align}$$

and

$$\begin{align} \left (z\frac{{\rm{d}}z} + b_k - 1 \right ){}_pF_q\left[ \begin{array}{c} a_1,\dots,a_p \\ b_1,\dots,b_k,\dots,b_q\end{array} ;z\right] &= (b_k - 1) \; {}_pF_q\left[ \begin{array}{c} a_1,\dots,a_p \\ b_1,\dots,b_k-1,\dots,b_q \end{array} ;z \right] \text{ for } b_k\neq 1 \end{align}$$

Additionally,

$$\begin{align} \frac{{\rm{d}}z} \; {}_pF_q\left[ \begin{array}{c} a_1,\dots,a_p \\ b_1,\dots,b_q \end{array} ;z \right] &= \frac{\prod_{i=1}^p a_i}{\prod_{j=1}^q b_j}\; {}_pF_q\left[ \begin{array}{c} a_1+1,\dots,a_p+1 \\ b_1+1,\dots,b_q+1 \end{array} ;z \right] \end{align}$$

Combining these gives a differential equation satisfied by w = pFq:
 * $$z\prod_{n=1}^{p}\left(z\frac{{\rm{d}}z} + a_n\right)w = z\frac{{\rm{d}}z}\prod_{n=1}^{q}\left(z\frac{{\rm{d}}z} + b_n-1\right)w$$.

Contiguous function and related identities
Take the following operator:
 * $$\vartheta = z\frac{{\rm{d}}z}.$$

From the differentiation formulas given above, the linear space spanned by
 * $${}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z), \vartheta\; {}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z)$$

contains each of
 * $${}_pF_q(a_1,\dots,a_j+1,\dots,a_p;b_1,\dots,b_q;z),$$
 * $${}_pF_q(a_1,\dots,a_p;b_1,\dots,b_k-1,\dots,b_q;z),$$
 * $$z\; {}_pF_q(a_1+1,\dots,a_p+1;b_1+1,\dots,b_q+1;z),$$
 * $${}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z).$$

Since the space has dimension 2, any three of these p+q+2 functions are linearly dependent:

(a_i-b_j+1){}_pF_q(...a_i..;...,b_j...;z) = a_i\,{}_pF_q(...a_i+1..;...,b_j...;z) -(b_j-1){}_pF_q(...a_i..;...,b_j-1...;z). $$

(a_i-a_j){}_pF_q(...a_i..a_j..;.....;z) = a_i\,{}_pF_q(...a_i+1..a_j..;......;z) -a_j{}_pF_q(...a_i..a_j+1...;....;z). $$

b_j{}_pF_q(...a_i....;..b_j...;z) = a_i\,{}_pF_q(...a_i+1....;..b_j+1...;z) +(b_j-a_i){}_pF_q(...a_i....;..b_j+1...;z) . $$

(a_i-1){}_pF_q(...a_i..a_j;...;z) = (a_i-a_j-1){}_pF_q(...a_i-1..a_j;...;z) +a_j{}_pF_q(...a_i-1..a_j+1;...;z) . $$

These dependencies can be written out to generate a large number of identities involving $${}_pF_q$$.

For example, in the simplest non-trivial case,
 * $$ \; {}_0F_1(a;z) = (1) \; {}_0F_1(a;z)$$,
 * $$ \; {}_0F_1(a-1;z) = (\frac{\vartheta}{a-1}+1) \; {}_0F_1(a;z)$$,
 * $$z \; {}_0F_1(a+1;z) = (a\vartheta) \; {}_0F_1(a;z)$$,

So
 * $$ \; {}_0F_1(a-1;z)- \; {}_0F_1(a;z) = \frac{z}{a(a-1)} \; {}_0F_1(a+1;z)$$.

This, and other important examples,

 * $$ \; {}_1F_1(a+1;b;z)- \, {}_1F_1(a;b;z) = \frac{z}{b} \; {}_1F_1(a+1;b+1;z)$$,
 * $$ \; {}_1F_1(a;b-1;z)- \, {}_1F_1(a;b;z) = \frac{az}{b(b-1)} \; {}_1F_1(a+1;b+1;z)$$,
 * $$ \; {}_1F_1(a;b-1;z)- \, {}_1F_1(a+1;b;z) = \frac{(a-b+1)z}{b(b-1)} \; {}_1F_1(a+1;b+1;z)$$
 * $$ \; {}_2F_1(a+1,b;c;z)- \, {}_2F_1(a,b;c;z) = \frac{bz}{c} \; {}_2F_1(a+1,b+1;c+1;z)$$,
 * $$ \; {}_2F_1(a+1,b;c;z)- \, {}_2F_1(a,b+1;c;z) = \frac{(b-a)z}{c} \; {}_2F_1(a+1,b+1;c+1;z)$$,
 * $$ \; {}_2F_1(a,b;c-1;z)- \, {}_2F_1(a+1,b;c;z) = \frac{(a-c+1)bz}{c(c-1)} \; {}_2F_1(a+1,b+1;c+1;z)$$,

can be used to generate continued fraction expressions known as Gauss's continued fraction.

Similarly, by applying the differentiation formulas twice, there are $$\binom{p+q+3}{2}$$ such functions contained in
 * $$\{1, \vartheta, \vartheta^2\}\; {}_p F_q (a_1,\dots,a_p;b_1,\dots,b_q;z),$$

which has dimension three so any four are linearly dependent. This generates more identities and the process can be continued. The identities thus generated can be combined with each other to produce new ones in a different way.

A function obtained by adding ±1 to exactly one of the parameters aj, bk in
 * $${}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z)$$

is called contiguous to
 * $${}_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;z).$$

Using the technique outlined above, an identity relating $${}_0F_1(a;z)$$ and its two contiguous functions can be given, six identities relating $${}_1F_1(a;b;z)$$ and any two of its four contiguous functions, and fifteen identities relating $${}_2F_1(a,b;c;z)$$ and any two of its six contiguous functions have been found. (The first one was derived in the previous paragraph. The last fifteen were given by Gauss in his 1812 paper.)

Identities
A number of other hypergeometric function identities were discovered in the nineteenth and twentieth centuries. A 20th century contribution to the methodology of proving these identities is the Egorychev method.

Saalschütz's theorem
Saalschütz's theorem is
 * $${}_3F_2 (a,b, -n;c, 1+a+b-c-n;1)= \frac{(c-a)_n(c-b)_n}{(c)_n(c-a-b)_n}.$$

For extension of this theorem, see a research paper by Rakha & Rathie.

Dixon's identity
Dixon's identity, first proved by, gives the sum of a well-poised 3F2 at 1:
 * $${}_3F_2 (a,b,c;1+a-b,1+a-c;1)= \frac{\Gamma(1+\frac{a}{2})\Gamma(1+\frac{a}{2}-b-c)\Gamma(1+a-b)\Gamma(1+a-c)}{\Gamma(1+a)\Gamma(1+a-b-c)\Gamma(1+\frac{a}{2}-b)\Gamma(1+\frac{a}{2}-c)}.$$

For generalization of Dixon's identity, see a paper by Lavoie, et al.

Dougall's formula
Dougall's formula gives the sum of a very well-poised series that is terminating and 2-balanced.
 * $$\begin{align}

{}_7F_6 & \left(\begin{matrix}a&1+\frac{a}{2}&b&c&d&e&-m\\&\frac{a}{2}&1+a-b&1+a-c&1+a-d&1+a-e&1+a+m\\ \end{matrix};1\right) = \\ &=\frac{(1+a)_m(1+a-b-c)_m(1+a-c-d)_m(1+a-b-d)_m}{(1+a-b)_m(1+a-c)_m(1+a-d)_m(1+a-b-c-d)_m}. \end{align}$$

Terminating means that m is a non-negative integer and 2-balanced means that
 * $$1+2a=b+c+d+e-m.$$

Many of the other formulas for special values of hypergeometric functions can be derived from this as special or limiting cases.

Generalization of Kummer's transformations and identities for 2F2
Identity 1.
 * $$e^{-x} \; {}_2F_2(a,1+d;c,d;x)= {}_2F_2(c-a-1,f+1;c,f;-x)$$

where
 * $$f=\frac{d(a-c+1)}{a-d}$$;

Identity 2.
 * $$e^{-\frac x 2} \, {}_2F_2 \left(a, 1+b; 2a+1, b; x\right)= {}_0F_1 \left(a+\tfrac{1}{2}; \tfrac {x^2} {16}\right) - \frac{x\left(1-\tfrac{2a} b\right)}{2(2a+1)}\; {}_0F_1 \left(a+\tfrac 3 2; \tfrac {x^2} {16}\right),$$

which links Bessel functions to 2F2; this reduces to Kummer's second formula for b = 2a:

Identity 3.
 * $$e^{-\frac x 2} \, {}_1F_1(a,2a,x)= {}_0F_1 \left (a+\tfrac 1 2; \tfrac{x^2}{16} \right )$$.

Identity 4.
 * $$\begin{align}

{}_2F_2(a,b;c,d;x)=& \sum_{i=0} \frac \; {}_1F_1(a+i;c+i;x)\frac{x^i}{i!} \\ =& e^x \sum_{i=0} \frac \; {}_1F_1(c-a;c+i;-x)\frac{x^i}{i!}, \end{align}$$ which is a finite sum if b-d is a non-negative integer.

Kummer's relation
Kummer's relation is
 * $${}_2F_1\left(2a,2b;a+b+\tfrac 1 2;x\right)= {}_2F_1\left(a,b; a+b+\tfrac 1 2; 4x(1-x)\right).$$

Clausen's formula
Clausen's formula
 * $${}_3F_2(2c-2s-1, 2s, c-\tfrac 1 2; 2c-1, c; x)=\, {}_2F_1(c-s-\tfrac 1 2,s; c; x)^2$$

was used by de Branges to prove the Bieberbach conjecture.

Special cases
Many of the special functions in mathematics are special cases of the confluent hypergeometric function or the hypergeometric function; see the corresponding articles for examples.

The series 0F0
As noted earlier, $${}_0F_0(z) = e^z$$. The differential equation for this function is $$\frac{d}{dz}w = w$$, which has solutions $$w = ke^z$$ where k is a constant.

The series 0F1
The functions of the form $${}_0F_1(a;z)$$ are called confluent hypergeometric limit functions and are closely related to Bessel functions.

The relationship is:
 * $$J_\alpha(x)=\frac{(\tfrac{x}{2})^\alpha}{\Gamma(\alpha+1)} {}_0F_1\left  (\alpha+1; -\tfrac{1}{4}x^2 \right ).$$
 * $$I_\alpha(x)=\frac{(\tfrac{x}{2})^\alpha}{\Gamma(\alpha+1)} {}_0F_1\left  (\alpha+1; \tfrac{1}{4}x^2 \right ).$$

The differential equation for this function is
 * $$w = \left (z\frac{d}{dz}+a \right )\frac{dw}{dz}$$

or
 * $$z\frac{d^2w}{dz^2}+a\frac{dw}{dz}-w = 0.$$

When a is not a positive integer, the substitution
 * $$w = z^{1-a}u,$$

gives a linearly independent solution
 * $$z^{1-a}\;{}_0F_1(2-a;z),$$

so the general solution is
 * $$k\;{}_0F_1(a;z)+l z^{1-a}\;{}_0F_1(2-a;z)$$

where k, l are constants. (If a is a positive integer, the independent solution is given by the appropriate Bessel function of the second kind.)

A special case is:
 * $${}_0F_1\left(\frac{1}{2};-\frac{z^2}{4}\right)=\cos z$$

The series 1F0
An important case is:
 * $${}_1F_0(a;;z) = (1-z)^{-a}.$$

The differential equation for this function is
 * $$\frac{d}{dz}w =\left (z\frac{d}{dz}+a \right )w,$$

or
 * $$(1-z)\frac{dw}{dz} = aw,$$

which has solutions
 * $$w=k(1-z)^{-a}$$

where k is a constant.

 * $${}_1F_0(1;;z) = \sum_{n \geqslant 0} z^n = (1-z)^{-1}$$ is the geometric series with ratio z and coefficient 1.

 * $$z ~ {}_1F_0(2;;z) = \sum_{n \geqslant 0} n z^n = z (1-z)^{-2}$$ is also useful.

The series 1F1
The functions of the form $${}_1F_1(a;b;z)$$ are called confluent hypergeometric functions of the first kind, also written $$M(a;b;z)$$. The incomplete gamma function $$\gamma(a,z)$$ is a special case.

The differential equation for this function is

 * $$\left (z\frac{d}{dz}+a \right )w = \left (z\frac{d}{dz}+b \right )\frac{dw}{dz}$$

or

 * $$z\frac{d^2w}{dz^2}+(b-z)\frac{dw}{dz}-aw = 0.$$

When b is not a positive integer, the substitution

 * $$w = z^{1-b}u,$$

gives a linearly independent solution

 * $$z^{1-b}\;{}_1F_1(1+a-b;2-b;z),$$

so the general solution is

 * $$k\;{}_1F_1(a;b;z)+l z^{1-b}\;{}_1F_1(1+a-b;2-b;z)$$

where k, l are constants.

When a is a non-positive integer, −n, $${}_1F_1(-n;b;z)$$ is a polynomial. Up to constant factors, these are the Laguerre polynomials. This implies Hermite polynomials can be expressed in terms of 1F1 as well.

The series 1F2
Relations to other functions are known for certain parameter combinations only.

The function $$x\; {}_1F_2\left(\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{x^2}{4}\right)$$ is the antiderivative of the cardinal sine. With modified values of $$a_1$$ and $$b_1$$, one obtains the antiderivative of $$\sin(x^\beta)/x^\alpha$$.

The Lommel function is $$ s_{\mu, \nu} (z) = \frac{z^{\mu + 1}}{(\mu - \nu + 1)(\mu + \nu + 1)} {}_1F_2(1; \frac{\mu}{2} - \frac{\nu}{2} + \frac{3}{2}, \frac{\mu}{2} + \frac{\nu}{2} + \frac{3}{2} ;-\frac{z^2}{4}) $$.

The series 2F0
The confluent hypergeometric function of the second kind can be written as:
 * $$U(a,b,z) = z^{-a} \; {}_2 F_0 \left( a, a-b+1; ; -\frac{1}{z}\right).$$

The series 2F1
Historically, the most important are the functions of the form $${}_2F_1(a,b;c;z)$$. These are sometimes called Gauss's hypergeometric functions, classical standard hypergeometric or often simply hypergeometric functions. The term Generalized hypergeometric function is used for the functions pFq if there is risk of confusion. This function was first studied in detail by Carl Friedrich Gauss, who explored the conditions for its convergence.

The differential equation for this function is

 * $$ \left (z\frac{d}{dz}+a \right ) \left (z\frac{d}{dz}+b \right )w =\left (z\frac{d}{dz}+c \right )\frac{dw}{dz}$$

or

 * $$z(1-z)\frac {d^2w}{dz^2} + \left[c-(a+b+1)z \right] \frac {dw}{dz} - ab\,w = 0.$$

It is known as the hypergeometric differential equation. When c is not a positive integer, the substitution

 * $$w = z^{1-c}u$$

gives a linearly independent solution

 * $$ z^{1-c}\; {}_2F_1(1+a-c,1+b-c;2-c;z),$$

so the general solution for |z| < 1 is

 * $$k\; {}_2F_1(a,b;c;z)+l z^{1-c}\; {}_2F_1(1+a-c,1+b-c;2-c;z)$$

where k, l are constants. Different solutions can be derived for other values of z. In fact there are 24 solutions, known as the Kummer solutions, derivable using various identities, valid in different regions of the complex plane.

When a is a non-positive integer, −n,
 * $${}_2F_1(-n,b;c;z)$$

is a polynomial. Up to constant factors and scaling, these are the Jacobi polynomials. Several other classes of orthogonal polynomials, up to constant factors, are special cases of Jacobi polynomials, so these can be expressed using 2F1 as well. This includes Legendre polynomials and Chebyshev polynomials.

A wide range of integrals of elementary functions can be expressed using the hypergeometric function, e.g.:

 * $$\int_0^x\sqrt{1+y^\alpha}\,\mathrm{d}y=\frac{x}{2+\alpha}\left \{\alpha\;{}_2F_1\left(\tfrac{1}{\alpha},\tfrac{1}{2};1+\tfrac{1}{\alpha};-x^\alpha \right) +2\sqrt{x^\alpha+1} \right \},\qquad \alpha\neq0.$$

The series 3F0
The Mott polynomials can be written as:
 * $$s_n(x)=(-x/2)^n{}_3F_0(-n,\frac{1-n}{2},1-\frac{n}{2};;-\frac{4}{x^2}).$$

The series 3F2
The function
 * $$\operatorname{Li}_2(x) = \sum_{n>0}\,{x^n}{n^{-2}} = x \; {}_3F_2(1,1,1;2,2;x)$$

is the dilogarithm

The function
 * $$Q_n(x;a,b,N)= {}_3F_2(-n,-x,n+a+b+1;a+1,-N+1;1)$$

is a Hahn polynomial.

The series 4F3
The function
 * $$p_n(t^2)=(a+b)_n(a+c)_n(a+d)_n \; {}_4F_3\left( -n, a+b+c+d+n-1, a-t, a+t ; a+b, a+c, a+d ;1\right)$$

is a Wilson polynomial.

All roots of a quintic equation can be expressed in terms of radicals and the Bring radical, which is the real solution to $$x^5 + x + a = 0$$. The Bring radical can be written as:
 * $$\operatorname{BR}(t) = -a \; {}_4F_3\left( \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5} ; \frac{1}{2}, \frac{3}{4}, \frac{5}{4} ; \frac{3125a^4}{256} \right).$$

The series q+1Fq
The functions
 * $$\operatorname{Li}_q(z)=z \; {}_{q+1}F_q\left(1,1,\ldots,1;2,2,\ldots,2;z\right)$$
 * $$\operatorname{Li}_{-p}(z)=z \; {}_pF_{p-1}\left(2,2,\ldots,2;1,1,\ldots,1;z\right)$$

for $$q\in\mathbb{N}_0$$ and $$p\in\mathbb{N}$$ are the Polylogarithm.

For each integer n≥2, the roots of the polynomial xn−x+t can be expressed as a sum of at most N−1 hypergeometric functions of type n+1Fn, which can always be reduced by eliminating at least one pair of a and b parameters.

Generalizations
The generalized hypergeometric function is linked to the Meijer G-function and the MacRobert E-function. Hypergeometric series were generalised to several variables, for example by Paul Emile Appell and Joseph Kampé de Fériet; but a comparable general theory took long to emerge. Many identities were found, some quite remarkable. A generalization, the q-series analogues, called the basic hypergeometric series, were given by Eduard Heine in the late nineteenth century. Here, the ratios considered of successive terms, instead of a rational function of n, are a rational function of qn. Another generalization, the elliptic hypergeometric series, are those series where the ratio of terms is an elliptic function (a doubly periodic meromorphic function) of n.

During the twentieth century this was a fruitful area of combinatorial mathematics, with numerous connections to other fields. There are a number of new definitions of general hypergeometric functions, by Aomoto, Israel Gelfand and others; and applications for example to the combinatorics of arranging a number of hyperplanes in complex N-space (see arrangement of hyperplanes).

Special hypergeometric functions occur as zonal spherical functions on Riemannian symmetric spaces and semi-simple Lie groups. Their importance and role can be understood through the following example: the hypergeometric series 2F1 has the Legendre polynomials as a special case, and when considered in the form of spherical harmonics, these polynomials reflect, in a certain sense, the symmetry properties of the two-sphere or, equivalently, the rotations given by the Lie group SO(3). In tensor product decompositions of concrete representations of this group Clebsch–Gordan coefficients are met, which can be written as 3F2 hypergeometric series.

Bilateral hypergeometric series are a generalization of hypergeometric functions where one sums over all integers, not just the positive ones.

Fox–Wright functions are a generalization of generalized hypergeometric functions where the Pochhammer symbols in the series expression are generalised to gamma functions of linear expressions in the index n.

title: Generalized hypergeometric function


text:
Streltsy

The streltsy (стрельцы,, lit. 'shooters/riflemen'; стрелец, ) were the units of Russian firearm infantry from the 16th century to the early 18th century and also a social stratum, from which personnel for streltsy troops were traditionally recruited. They are also collectively known as streletskoye voysko (стрелецкое войско, riflemen army). These infantry troops reinforced feudal levy horsemen or pomestnoye voysko (поместное войско). The first units were established by Ivan the Terrible as part of the first standing army in Russia.

Origins and organization
The first streltsy units were created by Ivan the Terrible sometime between 1545 and 1550 and armed with arquebuses. During his reign, Russia was fighting wars almost continuously, including the Livonian War against Scandinavia and the Polish–Lithuanian Commonwealth in the north and wars against the khanates of the south. They first saw combat at the siege of Kazan in 1552.

Tsar Ivan passed a decree on 1 October 1550 "on the stationing in Moscow and surrounding districts of one thousand service people," which is considered to be the formal founding of the streltsy regiments.

Initially, streltsy were recruited from among the free tradespeople and from the rural population. Later, military service in this unit became lifelong and hereditary. While earlier in the 16th century they had been an elite force, their effectiveness was reduced by poor training and lack of choice in recruiting. Streltsy were subdivided into "select" (выборные), later "Muscovite" (московские); and "municipal" (городские, in different Russian cities).

 * The Muscovite streltsy guarded the Kremlin, performed general guard duty, and participated in military operations. They also carried out general policing and fire brigade functions in Moscow. Grigory Kotoshikhin, a Russian diplomat who had spied for and then defected to the Swedish Empire in the 1660s, reported that they used axes and buckets and copper pumps as well as hooks to pull down adjacent buildings so that fires would not spread. Adam Olearius, a German who traveled to Russia in the 17th century, noted that they never used water.
 * The municipal streltsy performed garrison and border duty and carried out orders of the local government.

The streltsy came under the control of the Streletsky prikaz (стрелецкий приказ). In times of war, they came under their superiors. The municipal streltsy were also under the jurisdiction of the local voivodes (local governors or semi-independent rulers).

The largest military administrative unit of the streltsy forces was the Gear or Kit (прибор) that was later renamed prikazes (приказ) and in 1681 regiments (полк). The commanders of the streltsy (стрелецкие головы) and colonels in charge of regiments were chiefs of the Prikazy. They had to be nobles and appointed by the government.

Regiments were subdivided into "Hundreds" (сотни) and "Decades" (десятки). They could be dragoons or cavalry (стремянные) or footsoldiers (пешие).

Uniforms and equipment
The streltsy had identical uniforms, training and weapons. Uniforms consisted of red, yellow, blue or green coats (kaftans) with orange boots. Their primary weapon was an arquebus or musket, and they carried pollaxes or bardiches, and sabres for defense. Some units used pikes. The longer weapons were also used to support the arquebus or musket while firing.

Service conditions
The Russian government was chronically short of cash and so often did not pay the streltsy well. While "entitled" to an estimated four rubles a year in the 1550s, they were often allowed to farm or trade in order to supplement their incomes. This reduced their combat effectiveness and often their desire to go on campaigns, since a season campaigning meant loss of income.

The streltsy and their families lived in their own neighborhoods or districts settlements and received money and bread from the State Treasury. In certain locations, the streltsy were granted strips of land instead of money. The streltsy settlement in Moscow was located near where the main campus of Moscow State University now stands.

Military tactics
Military commanders deployed the streltsy in static formations, often against set formations or fortifications. They often fired from a platform and employed a mobile wooden "fortification" known in Russian as a "gulyay-gorod" (literally a "walking fort"). They reportedly fired in volley or caracole fashion, the first line firing and then stepping back to reload while the second line stepped forward to fire.

Politics
At the end of the 16th century, there were 20,000 to 25,000 streltsy. In 1681, there were 55,000, including 22,500 in Moscow alone. The engagements of the streltsy in handicrafts and trade led to a significant proprietary inequality among them and their blending with tradesmen. Even though the streltsy demonstrated their fighting efficiency on several occasions, such as during the siege of Kazan in 1552, the war with Livonia, the Northern Wars in the early 17th century, and military operations in Poland and Crimea, in the second half of the 17th century, the streltsy started to display their backwardness compared to the regular soldier or reiter regiments (see Imperial Russian Army).

Military service hardships, frequent salary delays, abuse on the part of local administration and commanders led to regular streltsy, especially the poorest ones, to participate in anti-serfdom uprisings in the 17th and early 18th centuries. These included the peasant wars in the Time of Troubles and after the last Rurikids were replaced by the Romanov tsars at the beginning of the 17th century and in 1670–1671 (such as by the cossacks of Stenka Razin), urban uprisings such as the Moscow uprising of 1682, the streltsy uprising of 1698, and the Bulavin Rebellion of 1705–1706 in Astrakhan.

At the same time, those streltsy who had been on top of the hierarchy enjoyed their social status and, therefore, tried to hold back the regular streltsy forces and keep them on the government’s side. In the late 17th century, the streltsy of Moscow began to actively participate in a struggle for power between different government groups, supporting the Old Believers and showing hostility towards any foreign innovations.

The streltsy became something of a "praetorian element" in Muscovite politics in the late 17th century. In 1682, they attempted to prevent Peter I from coming to the throne in favor of his half-brother, Ivan V.

Disbandment

After the fall of Sophia Alekseyevna in 1689, the government of Peter I engaged in a process of gradual limitation of the streltsy's military and political influence. Eight Moscow regiments were removed from the city and transferred to Belgorod, Sevsk, and Kiev.

In spite of these measures, the streltsy revolted yet again during the Grand Embassy of Peter the Great in Europe. Although the revolt was put down by the Scottish general Patrick Gordon who had entered Russian service under Alexis I in 1661 even before the tsar's return to Russia, Peter cut short his embassy and returned to crush the streltsy with reprisals, including public executions and torture.

Tortures included roasting the bare back, tearing flesh with iron hooks, and crushing feet in wooden presses called butuks. Executions included being broken on the wheel and being buried alive. Many of the bodies were hung around Novodevichy Convent where Sophia Alekseyevna and Eudoxia were confined for aiding the rebellion.

The corps was technically abolished in 1689. After having suffered a defeat at Narva in 1700, the government stopped their disbandment. The most efficient streltsy regiments took part in the most important military operations of the Great Northern War and in Peter’s Pruth River Campaign of 1711. Gradually, the streltsy were incorporated into the regular army. At the same time, the Municipal Streltsy started to be disbanded.

The liquidation of most streltsy units was finished in the 1720s. The Municipal Streltsy were kept in some cities until the late 18th century.

The Preobrazhensky Regiment and the Semyonovsky Regiment of the Imperial Guard replaced the streltsy and the traditional ryndy as the tsar's bodyguards.

title: Streltsy