(Q21028472)

English

hypergeometric function

special function defined by a hypergeometric series

gaussian hypergeometric function
ordinary hypergeometric function

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Statements

instance of

function

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special function

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hypergeometric series

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generalized hypergeometric function

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image

Plot of the hypergeometric function 2F1(a,b; c; z) with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
785 × 701; 917 KB

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named after

Carl Friedrich Gauss

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defining formula

\mathrm {F} (a,b,c;z)=\sum _{n=0}^{\infty }{\frac {(a)_{n}(b)_{n}}{(c)_{n}}}{\frac {z^{n}}{n!}},-c\notin {\boldsymbol {\mathsf {N}}}

1 reference

stated in

ISO 80000-2:2019 Quantities and units — Part 2: Mathematics

section, verse, paragraph, or clause

2-20.13

\mathrm {F} (a,b,c;z)={}_{2}\mathrm {F} _{1}(a,b;c;z)

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in defining formula

\mathrm {F} (a,b,c;z)

symbol represents

hypergeometric function

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(a)_{k}

symbol represents

Pochhammer symbol

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n!

symbol represents

factorial

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{}_{p}\mathrm {F} _{q}\left(a_{1},a_{2},\ldots ,a_{p};b_{1},b_{2},\ldots ,b_{q};z\right)

symbol represents

generalized hypergeometric function

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{\boldsymbol {\mathsf {N}}}

symbol represents

set of non-negative integers

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described by source

Great Soviet Encyclopedia (1926–1947)

statement is subject of

Q98708708

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ISO 80000-2:2019 Quantities and units — Part 2: Mathematics

section, verse, paragraph, or clause

2-20.13

subject named as

hypergeometric function

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maintained by WikiProject

WikiProject Mathematics

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Stack Exchange tag

https://mathoverflow.net/tags/hypergeometric-functions

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https://math.stackexchange.com/tags/hypergeometric-function

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different from

hypergeometric series

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inferred from

hypergeometric series

Identifiers

National Library of Israel J9U ID

987007553157805171

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stated in

National Library of Israel Names and Subjects Authority File

NL CR AUT ID

ph161655

subject named as

hypergeometrické funkce

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Encyclopædia Britannica Online ID

topic/hypergeometric-function

subject named as

hypergeometric function

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Encyclopedia of Mathematics article ID

Hypergeometric_function

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Freebase ID

/m/06hygx

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JSTOR topic ID (archived)

hypergeometric-functions

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MathWorld ID

HypergeometricFunction

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Microsoft Academic ID

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

ProofWiki ID

Definition:Hypergeometric_Function/Gaussian

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ScienceDirect topic ID

physics-and-astronomy/hypergeometric-functions

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mathematics/hypergeometric-function

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Sitelinks

Wikipedia(14 entries)

dewiki Gaußsche hypergeometrische Funktion
enwiki Hypergeometric function
eswiki Función hipergeométrica
frwiki Fonction hypergéométrique
hewiki פונקציה היפרגאומטרית
idwiki Fungsi hipergeometris
jawiki 超幾何関数
pmswiki Serie ipergeométrica ëd Gauss
ruwiki Гипергеометрическая функция
slwiki Hipergeometrična funkcija
svwiki Hypergeometriska funktionen
ukwiki Гіпергеометрична функція
zh_yuewiki 高斯超幾何函數
zhwiki 超几何函数

(Q21028472)

hypergeometric function

Statements

Identifiers

Sitelinks

Wikipedia(14 entries)

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