Generalized hypergeometric function: Specific values (formula 07.31.03.0142)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₇F₆

http://functions.wolfram.com/07.31.03.0142.01

Input Form

HypergeometricPFQ[{1/2, 1/2, 1, d, d, 1 - d, 1 - d}, {3/2, 3/2, 1 + d, 1 + d, 2 - d, 2 - d}, 1] == (1/(-1 + 2 d)^5) ((-1 + d)^2 d^2 Pi Csc[d Pi]^2 (-2 Pi + 4 d Pi - (-1 + 2 d) Pi Cos[2 d Pi] + 3 Sin[2 d Pi])) /; d != 1/2

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]