Gauss hypergeometric function 2F1: Transformations (formula 07.23.16.0006)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/07.23.16.0006.01

Input Form

Hypergeometric2F1[a, b, c, g z] Hypergeometric2F1[\[Alpha], \[Beta], \[Gamma], h z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] /; Subscript[c, k] == ((h^k Pochhammer[\[Alpha], k] Pochhammer[\[Beta], k])/ (k! Pochhammer[\[Gamma], k])) HypergeometricPFQ[ {-k, 1 - \[Gamma] - k, a, b}, {1 - \[Alpha] - k, 1 - \[Beta] - k, c}, g/h] || Subscript[c, k] == ((g^k Pochhammer[a, k] Pochhammer[b, k])/ (k! Pochhammer[c, k])) HypergeometricPFQ[{-k, 1 - c - k, \[Alpha], \[Beta]}, {1 - a - k, 1 - b - k, \[Gamma]}, h/g]

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]