Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3197)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3, b₁=1/2

http://functions.wolfram.com/07.27.03.3197.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 3}, {1/2, 1/2}, z] == (2048 + 164640 z + 352275 z^2 + 17325 z^3)/2048 + (1575 (-22 Sqrt[z] - 83 z^(3/2) + 94 z^(5/2) + 11 z^(7/2)) Log[1 - Sqrt[z]])/4096 - (1575 (-22 Sqrt[z] - 83 z^(3/2) + 94 z^(5/2) + 11 z^(7/2)) Log[1 + Sqrt[z]])/4096 - (1575 (5 Sqrt[z] + 70 z^(3/2) + 63 z^(5/2)) PolyLog[2, -Sqrt[z]])/2048 + (1575 (5 Sqrt[z] + 70 z^(3/2) + 63 z^(5/2)) PolyLog[2, Sqrt[z]])/2048

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]