Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7937)

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=3/2, a₃>=3/2

For fixed z and a₁=-7/2, a₂=3/2, a₃=7/2

For fixed z and a₁=-7/2, a₂=3/2, a₃=7/2, b₁=3

http://functions.wolfram.com/07.27.03.7937.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 7/2}, {3, 3}, z] == -((1/(36018675 Pi^2 z^2)) (512 (-163877 + 412958 z - 1954734 z^2 + 2731136 z^3 - 1685504 z^4 + 393216 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^ 2)) - (1/(36018675 Pi^2 z^2)) (512 Sqrt[1 - z] (115367 - 196140 z + 437904 z^2 - 350720 z^3 + 98304 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(36018675 Pi^2 z^2)) (512 (-163877 + 412958 z - 1954734 z^2 + 2731136 z^3 - 1685504 z^4 + 393216 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(36018675 Pi^2 z^2)) (256 Sqrt[1 - z] (115367 - 196140 z + 437904 z^2 - 350720 z^3 + 98304 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(36018675 Pi^2 z^2)) (256 (115367 - 241696 z + 1042851 z^2 - 1412864 z^3 + 855040 z^4 - 196608 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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type='integer'> 196140 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 115367 </cn> </apply> <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> <apply> <ci> EllipticE </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> 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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]