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

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=5/2, a₃>=5/2

For fixed z and a₁=2, a₂=5/2, a₃=4

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

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

Input Form

HypergeometricPFQ[{2, 5/2, 4}, {-(3/2), -(1/2)}, -z] == (1/(96 (1 + z)^10)) (96 - 1600 z - 290080 z^2 + 8558400 z^3 - 31771920 z^4 + 27096216 z^5 - 4982355 z^6 + 51100 z^7 + 700 z^8) + (1155 (448 z^(5/2) - 4656 z^(7/2) + 9864 z^(9/2) - 5397 z^(11/2) + 630 z^(13/2)) ArcSinh[Sqrt[z]])/(32 (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]