Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0125)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving products of ₂F₁ with algebraic arguments

http://functions.wolfram.com/07.23.26.0125.01

Input Form

(z - 2 (1 + Sqrt[1 - z]))^a Hypergeometric2F1[a, b, c, (2 (1 + Sqrt[1 - z]))/z] Hypergeometric2F1[a, -b + c, c, (2 (1 + Sqrt[1 - z]))/z] == ((2^(1 - c) Sqrt[Pi] Gamma[c]^2)/ (Gamma[a] Gamma[b] Gamma[-a + c] Gamma[-b + c])) z^a MeijerG[{{1}, {c/2, (1 + c)/2, c}}, {{a, b, -a + c, -b + c}, {}}, -z]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]