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

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=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 5/2, 5/2}, {-(7/2), 4}, -z] == -((1/(105 Pi z^3 (1 + z)^7)) (32 (120120 + 811965 z + 2336985 z^2 + 3702381 z^3 + 3469803 z^4 + 1904274 z^5 + 551488 z^6 + 54656 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])) - (1/(105 Pi z^3 (1 + z)^(13/2))) (32 (120120 + 811965 z + 2336985 z^2 + 3702381 z^3 + 3469803 z^4 + 1904274 z^5 + 551488 z^6 + 54656 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(105 Pi z^3 (1 + z)^6)) (128 (30030 + 176715 z + 431025 z^2 + 556089 z^3 + 397701 z^4 + 146880 z^5 + 19648 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(105 Pi z^3 (1 + z)^(13/2))) (64 (60060 + 398475 z + 1121505 z^2 + 1728153 z^3 + 1562223 z^4 + 815112 z^5 + 218432 z^6 + 15360 z^7) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> 176715 </cn> <ci> z </ci> </apply> <cn type='integer'> 30030 </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> </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 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 105 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 15360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 218432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 815112 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1562223 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1728153 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1121505 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> 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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]