Generalized hypergeometric function: Specific values (formula 07.31.03.0141)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case ₇F₆

http://functions.wolfram.com/07.31.03.0141.01

Input Form

HypergeometricPFQ[{1, b, b, b, 2 - b, 2 - b, 2 - b}, {1 + b, 1 + b, 1 + b, 3 - b, 3 - b, 3 - b}, 1] == ((b^3 (2 - b)^3)/(16 (1 - b)^6)) (8 - 3 Pi^2 (1 - b)^2 Csc[Pi b]^2 + 3 Pi (1 - b) Cot[Pi b] + 2 Pi^3 (1 - b)^3 Cos[Pi b] Csc[Pi b]^3) /; b != 1

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]