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

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=1, a₂>=1

For fixed z and a₁=1, a₂=5/2, a₃>=5/2

For fixed z and a₁=1, a₂=5/2, a₃=4

For fixed z and a₁=1, a₂=5/2, a₃=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1, 5/2, 4}, {-(5/2), 7/2}, -z] == (-3840 - 22400 z - 53904 z^2 - 67728 z^3 - 44634 z^4 - 5145 z^5 - 3570 z^6 - 280 z^7)/(144 z^2 (1 + z)^6) + (5 (256 + 1664 z + 4576 z^2 + 6864 z^3 + 6006 z^4 + 3003 z^5) ArcSinh[Sqrt[z]])/(48 z^(5/2) (1 + z)^(13/2))

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]