Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8k9)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=4

For fixed z and a₁=-5/2, a₂=-5/2, a₃=4, b₁=-1/2

http://functions.wolfram.com/07.27.03.a8k9.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 4}, {-(1/2), -(1/2)}, z] == (1/64) (64 + 6400 z + 86025 z^2) + (75/64) (-229 z^(3/2) + 227 z^(5/2)) Log[1 - Sqrt[z]] - (75/64) (-229 z^(3/2) + 227 z^(5/2)) Log[1 + Sqrt[z]] - (4725/128) (5 z^(3/2) + 11 z^(5/2)) PolyLog[2, -Sqrt[z]] + (4725/128) (5 z^(3/2) + 11 z^(5/2)) 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]