Generalized hypergeometric function 4F3: Specific values (formula 07.28.03.0189)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Specific values

For fixed z

http://functions.wolfram.com/07.28.03.0189.01

Input Form

HypergeometricPFQ[{1, 1, 1, 1}, {3/2, 2, 2}, z] == (I/(3 z)) (2 ArcSin[Sqrt[z]]^3 - 6 I ArcSin[Sqrt[z]]^2 Log[1 - E^(-2 I ArcSin[Sqrt[z]])] + 6 ArcSin[Sqrt[z]] PolyLog[2, E^(-2 I ArcSin[Sqrt[z]])] - 3 I PolyLog[3, E^(-2 I ArcSin[Sqrt[z]])] + 3 I Zeta[3])

Standard Form

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MathML Form

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Rule Form

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Contributed by

Brychkov Yu.A. (2006)

Date Added to functions.wolfram.com (modification date)

2007-05-02

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,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]