Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ab7v)

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=2

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

http://functions.wolfram.com/07.27.03.ab7v.01

Input Form

HypergeometricPFQ[{-(5/2), 1, 2}, {-(1/2), -(1/2)}, -z] == (32 + 672 z + 450 Pi^2 z^(3/2) + 6700 z^2 + 2025 Pi^2 z^(5/2) + 6300 z^3 + 1575 Pi^2 z^(7/2))/(32 (1 + z)) + (1/(1536 (1 + z)^(13/2))) ((-1536 - 55824 z - 1175016 z^2 - 7406074 z^3 - 21972101 z^4 - 37394260 z^5 - 38573295 z^6 - 23953530 z^7 - 8268720 z^8 - 1222560 z^9) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1536 (1 + z)^(13/2))) ((1536 + 55824 z + 1175016 z^2 + 7406074 z^3 + 21972101 z^4 + 37394260 z^5 + 38573295 z^6 + 23953530 z^7 + 8268720 z^8 + 1222560 z^9) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (61 z^(3/2) + 170 z^(5/2) + 105 z^(7/2)) Log[Sqrt[z] + Sqrt[1 + z]])/ (8 (1 + z)^(3/2)) + (1/(1536 (1 + z)^(13/2))) ((1536 + 55824 z + 1175016 z^2 + 7406074 z^3 + 21972101 z^4 + 37394260 z^5 + 38573295 z^6 + 23953530 z^7 + 8268720 z^8 + 1222560 z^9) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225/8) (2 z^(3/2) + 7 z^(5/2)) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (225/8) (2 z^(3/2) + 7 z^(5/2)) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (225/8) (2 z^(3/2) + 7 z^(5/2)) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + 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]