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

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, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=3

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

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

Input Form

HypergeometricPFQ[{3/2, 3, 3}, {-(7/2), -(5/2)}, -z] == (1/(2240 (1 + z)^13)) (2240 + 25664 z + 148224 z^2 - 106112 z^3 - 123389120 z^4 + 5960960832 z^5 - 40340045824 z^6 + 75757551584 z^7 - 45277370424 z^8 + 7956007059 z^9 - 270541194 z^10) + (1287 (18304 z^(9/2) - 314496 z^(11/2) + 1245600 z^(13/2) - 1571240 z^(15/2) + 665577 z^(17/2) - 83160 z^(19/2) + 1848 z^(21/2)) ArcSinh[Sqrt[z]])/(64 Sqrt[1 + z] (1 + 13 z + 78 z^2 + 286 z^3 + 715 z^4 + 1287 z^5 + 1716 z^6 + 1716 z^7 + 1287 z^8 + 715 z^9 + 286 z^10 + 78 z^11 + 13 z^12 + z^13))

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]