Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.aee6)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=-3/2, a₃>=-3/2

For fixed z and a₁=-3/2, a₂=-3/2, a₃=4

For fixed z and a₁=-3/2, a₂=-3/2, a₃=4, b₁=-1/2

http://functions.wolfram.com/07.27.03.aee6.01

Input Form

HypergeometricPFQ[{-(3/2), -(3/2), 4}, {-(1/2), 3/2}, z] == (1/512) (467 - 4899 z) - (3 (15 - 420 z + 373 z^2) Log[1 - Sqrt[z]])/ (1024 Sqrt[z]) + (3 (15 - 420 z + 373 z^2) Log[1 + Sqrt[z]])/ (1024 Sqrt[z]) + (945/256) z^(3/2) PolyLog[2, -Sqrt[z]] - (945/256) z^(3/2) PolyLog[2, Sqrt[z]]

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)

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