Regularized hypergeometric function 2F1: Transformations (formula 07.24.16.0007)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/07.24.16.0007.01

Input Form

Hypergeometric2F1Regularized[a, b, c, g z] Hypergeometric2F1Regularized[ \[Alpha], \[Beta], \[Gamma], h z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] /; Subscript[c, k] == ((Gamma[1 - \[Alpha]] Gamma[1 - \[Beta]] h^k)/ (k! Gamma[\[Gamma] + k])) HypergeometricPFQRegularized[ {-k, 1 - \[Gamma] - k, a, b}, {1 - \[Alpha] - k, 1 - \[Beta] - k, c}, g/h] || Subscript[c, k] == ((Gamma[1 - a] Gamma[1 - b] g^k)/ (k! Gamma[c + k])) HypergeometricPFQRegularized[ {-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

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]