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

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=2, a₂>=2

For fixed z and a₁=2, a₂=2, a₃>=2

For fixed z and a₁=2, a₂=2, a₃=5/2

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

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

Input Form

HypergeometricPFQ[{2, 2, 5/2}, {-(7/2), -(1/2)}, -z] == (1/(28 (1 + z)^10)) (28 + 120 z - 2356 z^2 - 45504 z^3 - 910440 z^4 + 6225552 z^5 - 6200560 z^6 + 1228932 z^7 - 27107 z^8) + (495 (704 z^(9/2) - 2072 z^(11/2) + 1260 z^(13/2) - 161 z^(15/2) + 2 z^(17/2)) ArcSinh[Sqrt[z]])/(4 (1 + z)^(21/2))

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]