Wikidata is busy right now, so this page shows AIDb's saved copy from November 14, 2026. Live facts will be back shortly.
%20with%20a%3D2%20and%20b%3D3%20and%20c%3D4%20in%20the%20complex%20plane%20from%20-2-2i%20to%202%2B2i%20with%20colors%20created%20with%20Mathematica%2013.1%20function%20ComplexPlot3D.svg)
hypergeometric function
Special function defined by a hypergeometric series
Also known as gaussian hypergeometric function · ordinary hypergeometric function
- Instance of
- function
- , special function
- , hypergeometric series
- +1 more
Overview
All data
27 statements · 11% with external sources · numbers in brackets are citations
- 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}}\mathrm{F}(a, b, c; z) = {}_2\mathrm{F}_1(a, b; c; z)
- In defining formula
\mathrm{F}(a, b, c; z)symbol represents: hypergeometric function(a)_ksymbol represents: Pochhammer symboln!symbol represents: factorial{}_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\boldsymbol{\mathsf{N}}symbol represents: set of non-negative integers
On other databases
12 identifiers linking hypergeometric function across the web's reference databases
- Encyclopædia Britannica Online IDscience/hypergeometric-function
- Encyclopedia of Mathematics article IDHypergeometric_function
- Freebase ID/m/06hygx
- J9U entity ID987007553157805171
- JSTOR topic ID (archived)hypergeometric-functions
- MathWorld IDHypergeometricFunction
- Microsoft Academic ID (discontinued)197320386
- Namuwiki ID초기하함수
- NL CR AUT IDph161655
- OpenAlex IDC197320386
- ProofWiki IDDefinition:Hypergeometric_Function/Gaussian
- ScienceDirect topic IDphysics-and-astronomy/hypergeometric-functions