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

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=3, a₃>=3

For fixed z and a₁=1, a₂=3, a₃=3

For fixed z and a₁=1, a₂=3, a₃=3, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1, 3, 3}, {-(5/2), 4}, -z] == (-10395 - 48510 z - 88433 z^2 - 77116 z^3 - 30053 z^4 - 1470 z^5 - 105 z^6)/ (40 z^2 (1 + z)^5) + (3 (3465 + 18480 z + 39963 z^2 + 44154 z^3 + 25399 z^4 + 6508 z^5) ArcSinh[Sqrt[z]])/(20 z^(5/2) (1 + z)^(11/2)) - (2079 ArcSinh[Sqrt[z]]^2)/(8 z^3)

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]