Regularized generalized hypergeometric function: Specific values (formula 07.32.03.0148)

HypergeometricPFQRegularized

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₇F^~₆

http://functions.wolfram.com/07.32.03.0148.01

Input Form

HypergeometricPFQRegularized[{1, 3/2, 3/2, d, d, 1 - d, 1 - d}, {1/2, 1/2, 1 + d, 1 + d, 2 - d, 2 - d}, -1] == (Sin[d Pi]^2/((1 - 2 d) Pi^3)) (-2 Pi Csc[d Pi] - 2 PolyGamma[d/2] + 2 PolyGamma[(1 + d)/2] + ((2 d - 1)/2) (2 Pi^2 Cot[d Pi] Csc[d Pi] - PolyGamma[1, d/2] + PolyGamma[1, (1 + d)/2])) /; 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

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]