Generalized hypergeometric function: Specific values (formula 07.31.03.0152)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₉F₈

http://functions.wolfram.com/07.31.03.0152.01

Input Form

HypergeometricPFQ[{-n, 1, 3/2, 3/2, 3/2, f, g, 1 - f, 1 - g}, {1/2, 1/2, 1/2, n + 2, 1 + f, 2 - f, 1 + g, 2 - g}, 1] == ((n! (n + 1)!)/((f + g - 1) (f - g))) (((2 g - 1)^2 f (f - 1))/(Pochhammer[g + 1, n] Pochhammer[2 - g, n]) - ((2 f - 1)^2 g (g - 1))/(Pochhammer[f + 1, n] Pochhammer[2 - f, n])) /; 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]