Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0169)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₂F^~₁with algebraic arguments

http://functions.wolfram.com/07.23.26.0169.01

Input Form

Hypergeometric2F1[a, b, (a + b + 1)/2, (1 - Sqrt[1 + z])/2] Hypergeometric2F1Regularized[a, b, (a + b + 1)/2, (1 - Sqrt[1 + z])/2] == ((2^(a + b - 1) Gamma[(a + b + 1)/2])/(Sqrt[Pi] Gamma[a] Gamma[b])) MeijerG[{{1 - a, 1 - b, 1 + (-a - b)/2}, {}}, {{0}, {(1 - a - b)/2, 1 - a - b}}, 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]