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

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=4

For fixed z and a₁=3/2, a₂=3, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 3, 4}, {-(5/2), -(5/2)}, -z] == (1/(3200 (1 + z)^13)) (3200 + 32384 z + 232192 z^2 - 12808448 z^3 + 2340505344 z^4 - 32183542400 z^5 + 107366396384 z^6 - 111648831008 z^7 + 36362045577 z^8 - 2884387506 z^9 + 10672200 z^10) + (9009 (4224 z^(7/2) - 171776 z^(9/2) + 1245600 z^(11/2) - 2672800 z^(13/2) + 1934075 z^(15/2) - 447876 z^(17/2) + 24024 z^(19/2)) ArcSinh[Sqrt[z]])/(640 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]