Generalized hypergeometric function 4F3: Identities (formula 07.28.17.0030)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Identities

Functional identities

Functional identities for z==1

http://functions.wolfram.com/07.28.17.0030.01

Input Form

HypergeometricPFQ[{-n, b, c, 1 - b}, {e, 1 - c - n, 1 + 2 c - e}, 1] == ((Pochhammer[(b + e - 1)/2, n] Pochhammer[(e - b)/2, n] Pochhammer[2 c, n])/ (Pochhammer[c, n] Pochhammer[c + 1/2, n] Pochhammer[e, n])) HypergeometricPFQ[{-n, 1 + c - (b + e)/2, c + (1 + b - e)/2, 1 - e - n}, {(3 - b - e)/2 - n, 1 + (b - e)/2 - n, 1 + 2 c - e}, 1] /; Element[n, Integers] && n >= 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]