Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.au9q)

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=-5/2

http://functions.wolfram.com/07.27.03.au9q.01

Input Form

HypergeometricPFQ[{5/2, 3, 3}, {-(5/2), -(5/2)}, -z] == (1/(320 (1 + z)^13)) (320 + 3008 z + 24320 z^2 - 1962368 z^3 + 369569216 z^4 - 5409849664 z^5 + 19620987584 z^6 - 23004247200 z^7 + 9077035506 z^8 - 1055752467 z^9 + 22452738 z^10) - (693 (-8448 z^(7/2) + 361856 z^(9/2) - 2805696 z^(11/2) + 6591200 z^(13/2) - 5439390 z^(15/2) + 1561329 z^(17/2) - 131208 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]