Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1526)

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=-7/2, a₂>=-7/2

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

For fixed z and a₁=-7/2, a₂=-7/2, a₃=1

For fixed z and a₁=-7/2, a₂=-7/2, a₃=1, b₁=5/2

http://functions.wolfram.com/07.27.03.1526.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1}, {5/2, 4}, -z] == (2 (-8 - 676 z + 20449 z^2))/(184041 z^3) + (1/(3769159680 z^3)) (Sqrt[1 + z] (327680 + 27525120 z - 716042505 z^2 + 2755354720 z^3 - 2758626516 z^4 + 734493408 z^5 - 35710816 z^6)) + (7 (-3003 + 30030 z - 68640 z^2 + 45760 z^3 - 8320 z^4 + 256 z^5) ArcSinh[Sqrt[z]])/(585728 z^(3/2))

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]