Generalized hypergeometric function: Specific values (formula 07.31.03.0143)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₇F₆

http://functions.wolfram.com/07.31.03.0143.01

Input Form

HypergeometricPFQ[{1, 1, 1, d, d, 2 - d, 2 - d}, {2, 2, 1 + d, 1 + d, 3 - d, 3 - d}, 1] == (((-2 + d)^2 d^2 Csc[d Pi]^2)/(24 (-1 + d)^6)) (-12 + 8 Pi^2 - 16 d Pi^2 + 8 d^2 Pi^2 - 2 (-6 + (-1 + d)^2 Pi^2) Cos[2 d Pi] + 9 (-1 + d) Pi Sin[2 d Pi])

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]