Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.asf2)

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=3

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

http://functions.wolfram.com/07.27.03.asf2.01

Input Form

HypergeometricPFQ[{3/2, 3, 3}, {-(5/2), -(1/2)}, -z] == (1/(320 (1 + z)^10)) (320 - 256 z - 112320 z^2 - 4622720 z^3 + 59321200 z^4 - 108205200 z^5 + 43323119 z^6 - 2882530 z^7) + (693 (4752 z^(7/2) - 24464 z^(9/2) + 26601 z^(11/2) - 6888 z^(13/2) + 280 z^(15/2)) ArcSinh[Sqrt[z]])/(64 (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]