Generalized hypergeometric function: Identities (formula 07.31.17.0011)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Identities

Functional identities

Relations between contiguous functions

http://functions.wolfram.com/07.31.17.0011.01

Input Form

Product[Subscript[b, k], {k, 2, q}] (c HypergeometricPFQ[{a, b, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] - a HypergeometricPFQ[{a + 1, b + 1, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c + 1, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] - (c - a) HypergeometricPFQ[ {a, b + 1, Subscript[a, 3], \[Ellipsis], Subscript[a, p]}, {c + 1, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z]) + z a Product[Subscript[a, j], {j, 3, p}] HypergeometricPFQ[ {a + 1, b + 1, Subscript[a, 3] + 1, \[Ellipsis], Subscript[a, p] + 1}, {c + 1, Subscript[b, 2] + 1, \[Ellipsis], Subscript[b, q] + 1}, z] == 0

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]