Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3104)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.3104.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 5/2}, {1, 4}, z] == (1/(156080925 Pi^2 z^3)) (128 (-11200 + 48650 z + 315350 z^2 + 71745826 z^3 + 203169937 z^4 + 68756536 z^5 + 633600 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(156080925 Pi^2 z^3)) (128 Sqrt[1 - z] (11200 - 45850 z - 325500 z^2 - 36458056 z^3 - 79498721 z^4 - 20021760 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (128 (11200 - 48650 z - 315350 z^2 - 71745826 z^3 - 203169937 z^4 - 68756536 z^5 - 633600 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (64 Sqrt[1 - z] (-11200 + 45850 z + 325500 z^2 + 36458056 z^3 + 79498721 z^4 + 20021760 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(156080925 Pi^2 z^3)) (64 (-11200 + 51450 z + 303625 z^2 + 46046656 z^3 + 122209173 z^4 + 39403508 z^5 + 316800 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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<ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 79498721 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36458056 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 325500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 45850 </cn> <ci> z </ci> </apply> <cn type='integer'> -11200 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 156080925 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 316800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 39403508 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 122209173 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 46046656 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </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]