Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.auw0)

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, a₂>=3

For fixed z and a₁=3, a₂=3, a₃>=3

For fixed z and a₁=3, a₂=3, a₃=4

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

http://functions.wolfram.com/07.27.03.auw0.01

Input Form

HypergeometricPFQ[{3, 3, 4}, {-(5/2), 3}, -z] == (640 + 8832 z + 71168 z^2 + 758272 z^3 - 2352747 z^4 + 771542 z^5 - 9240 z^6)/(640 (1 + z)^9) - (9009 (33 z^(7/2) - 44 z^(9/2) + 8 z^(11/2)) ArcSinh[Sqrt[z]])/(128 (1 + z)^(19/2))

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]