Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au9e)

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=3, a₃>=3

For fixed z and a₁=5/2, a₂=3, a₃=3

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

http://functions.wolfram.com/07.27.03.au9e.01

Input Form

HypergeometricPFQ[{5/2, 3, 3}, {-(7/2), 1/2}, -z] == (1/(448 (1 + z)^11)) (448 + 10688 z + 131008 z^2 + 1293888 z^3 + 20359680 z^4 - 126201768 z^5 + 128751992 z^6 - 30232901 z^7 + 1167014 z^8) - (6435 (1144 z^(9/2) - 3224 z^(11/2) + 2079 z^(13/2) - 328 z^(15/2) + 8 z^(17/2)) ArcSinh[Sqrt[z]])/ (64 Sqrt[1 + z] (1 + 11 z + 55 z^2 + 165 z^3 + 330 z^4 + 462 z^5 + 462 z^6 + 330 z^7 + 165 z^8 + 55 z^9 + 11 z^10 + z^11))

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]