Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.atz5)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5/2, a₃>=5/2

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

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

http://functions.wolfram.com/07.27.03.atz5.01

Input Form

HypergeometricPFQ[{5/2, 5/2, 5/2}, {-(5/2), 4}, -z] == -((1/(45 Pi z^3 (1 + z)^6)) (32 (27720 + 159705 z + 379925 z^2 + 475399 z^3 + 326763 z^4 + 113928 z^5 + 13344 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])) - (1/(45 Pi z^3 (1 + z)^(11/2))) (32 (27720 + 159705 z + 379925 z^2 + 475399 z^3 + 326763 z^4 + 113928 z^5 + 13344 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(45 Pi z^3 (1 + z)^5)) (64 (13860 + 67725 z + 131350 z^2 + 125637 z^3 + 58296 z^4 + 9504 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(45 Pi z^3 (1 + z)^(11/2))) (128 (6930 + 39060 z + 90425 z^2 + 109206 z^3 + 71415 z^4 + 23064 z^5 + 1920 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 326763 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 475399 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 379925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 159705 </cn> <ci> z </ci> </apply> <cn type='integer'> 27720 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 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</apply> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 9504 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 125637 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 131350 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 67725 </cn> <ci> z </ci> </apply> <cn type='integer'> 13860 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> 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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]