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

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=1/2, a₃>=1/2

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

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

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

Input Form

HypergeometricPFQ[{-(5/2), 1/2, 1/2}, {1, 4}, z] == (128 (-64 + 542 z - 2719 z^2 + 2719 z^3 - 542 z^4 + 64 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 z^3) + (1/(51975 Pi^2 z^3)) (128 Sqrt[1 - z] (64 - 526 z + 2595 z^2 - 124 z^3 + 16 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(51975 Pi^2 z^3)) (128 (64 - 542 z + 2719 z^2 - 2719 z^3 + 542 z^4 - 64 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (64 Sqrt[1 - z] (-64 + 526 z - 2595 z^2 + 124 z^3 - 16 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 z^3) + (64 (-64 + 558 z - 2852 z^2 + 4624 z^3 - 273 z^4 + 32 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 z^3)

Standard Form

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MathML Form

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</cn> <apply> <times /> <cn type='integer'> 2595 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 526 </cn> <ci> z </ci> </apply> <cn type='integer'> -64 </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> <power /> <apply> <times /> <cn type='integer'> 51975 </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> 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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]