Generalized hypergeometric function 4F3: Identities (formula 07.28.17.0017)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Identities

Functional identities

Relations between contiguous functions

http://functions.wolfram.com/07.28.17.0017.01

Input Form

HypergeometricPFQ[{a, b, c, Subscript[a, 4]}, {d, e, Subscript[b, 3]}, z] - ((a b (d - c) (e - c))/(d e (a - c) (b - c))) HypergeometricPFQ[{a + 1, b + 1, c, Subscript[a, 4]}, {d + 1, e + 1, Subscript[b, 3]}, z] - ((a c (d - b) (e - b))/(d e (a - b) (c - b))) HypergeometricPFQ[{a + 1, b, c + 1, Subscript[a, 4]}, {d + 1, e + 1, Subscript[b, 3]}, z] - ((b c (d - a) (e - a))/(d e (b - a) (c - a))) HypergeometricPFQ[{a, b + 1, c + 1, Subscript[a, 4]}, {d + 1, e + 1, Subscript[b, 3]}, z] == 0

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},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,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]