Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0100)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases for products of ₂F₁ with linear arguments

http://functions.wolfram.com/07.23.26.0100.01

Input Form

Hypergeometric2F1[a, b, a + b + 1/2, -z] Hypergeometric2F1[1/2 - a, 1/2 - b, 3/2 - a - b, -z] == (((1 - 2 a - 2 b) Cos[Pi (a - b)])/ (2 Sqrt[Pi] Cos[Pi (a + b)])) MeijerG[{{1/2, 1/2 + a - b, 1/2 + b - a}, {}}, {{0}, {1/2 - a - b, a + b - 1/2}}, 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]