Generalized hypergeometric function: Identities (formula 07.31.17.0016)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]

Identities

Functional identities

Relations of special kind

http://functions.wolfram.com/07.31.17.0016.01

Input Form

HypergeometricPFQ[{a, Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {-a, 1 + a, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] - 2 HypergeometricPFQ[{a, Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {1 - a, 1 + a, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z] == -HypergeometricPFQ[{Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {1 - a, Subscript[b, 3], \[Ellipsis], Subscript[b, q]}, z]

Standard Form

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MathML 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},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]