Generalized hypergeometric function: Specific values (formula 07.31.03.0139)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₇F₆

http://functions.wolfram.com/07.31.03.0139.01

Input Form

HypergeometricPFQ[{-n, 1, 3/2, d, e, 1 - d, 1 - e}, {1/2, 2 + n, 1 + d, 2 - d, 1 + e, 2 - e}, 1] == (((-1)^n n! (n + 1)! d e (1 - d) (1 - e))/((d - e) (1 - d - e))) (Gamma[-n - d]/Gamma[2 + n - d] - Gamma[-n - e]/Gamma[2 + n - e]) /; 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},{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]