hypergeometric function (Q3122)

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special function defined by a hypergeometric series

gaussian hypergeometric function
ordinary hypergeometric function

Language	Label	Description	Also known as
English	hypergeometric function	special function defined by a hypergeometric series	gaussian hypergeometric function ordinary hypergeometric function

Statements

Q21028472

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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

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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hypergeometric-functions

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hypergeometric series

1 reference

hypergeometric series

Encyclopædia Britannica Online ID

topic/hypergeometric-function

subject named as

hypergeometric function

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Microsoft Academic ID

197320386

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described by source

Great Soviet Encyclopedia (1926–1947)

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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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/m/06hygx

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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

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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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C197320386

1 reference

26 January 2022

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

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special function

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hypergeometric series

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generalized hypergeometric function

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ph161655

subject named as

hypergeometrické funkce

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ScienceDirect topic ID

physics-and-astronomy/hypergeometric-functions

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mathematics/hypergeometric-function

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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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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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Encyclopedia of Mathematics article ID

Hypergeometric_function

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HypergeometricFunction

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Definition:Hypergeometric_Function/Gaussian

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National Library of Israel J9U ID

987007553157805171

1 reference

National Library of Israel Names and Subjects Authority File

Sitelinks

⧼wikibase-sitelinks-mathematics⧽(0 entries)

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