Generalized hypergeometric function 2F3: Identities (formula 07.26.17.0015)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Identities

Functional identities

Relations between contiguous functions

http://functions.wolfram.com/07.26.17.0015.01

Input Form

HypergeometricPFQ[{a + 1, b + 1}, {c + 1, d + 1, e + 1}, z] - ((c d (a - e) (b - e))/(a b (c - e) (d - e))) HypergeometricPFQ[{a, b}, {c, d, e + 1}, z] - ((c e (a - d) (b - d))/(a b (c - d) (e - d))) HypergeometricPFQ[{a, b}, {c, d + 1, e}, z] - ((d e (a - c) (b - c))/(a b (d - c) (e - c))) HypergeometricPFQ[{a, b}, {c + 1, d, e}, 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,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]