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

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=4, a₃>=4

For fixed z and a₁=5/2, a₂=4, a₃=4

For fixed z and a₁=5/2, a₂=4, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 4, 4}, {-(7/2), 7/2}, -z] == (1/(5376 z^2 (1 + z)^10)) (-15360 - 151040 z - 661376 z^2 - 1667520 z^3 - 2478120 z^4 - 880260 z^5 + 17281155 z^6 - 46534696 z^7 + 9387860 z^8) - (5 (-1024 - 10752 z - 51072 z^2 - 144704 z^3 - 271320 z^4 - 352716 z^5 - 323323 z^6 + 2092662 z^7 - 2378376 z^8 + 240240 z^9) ArcSinh[Sqrt[z]])/ (1792 Sqrt[1 + z] (z^(5/2) + 10 z^(7/2) + 45 z^(9/2) + 120 z^(11/2) + 210 z^(13/2) + 252 z^(15/2) + 210 z^(17/2) + 120 z^(19/2) + 45 z^(21/2) + 10 z^(23/2) + z^(25/2)))

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]