Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a82j)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-11/2, b>=a

For fixed z and a=-11/2, b=15/4

http://functions.wolfram.com/07.23.03.a82j.01

Input Form

Hypergeometric2F1[-(11/2), 15/4, 1, z] == (1/(55440 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (2 (334016 - 4685168 z + 18918960 z^2 - 32354400 z^3 + 24995100 z^4 - 7210125 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (334016 - 4685168 z + 18918960 z^2 - 32354400 z^3 + 24995100 z^4 - 7210125 z^5) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-112256 + 82960 z + 4985760 z^2 - 16972800 z^3 + 19227000 z^4 - 7210125 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-334016 + 4685168 z - 18918960 z^2 + 32354400 z^3 - 24995100 z^4 + 7210125 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-334016 + 4685168 z - 18918960 z^2 + 32354400 z^3 - 24995100 z^4 + 7210125 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-334016 + 4685168 z - 18918960 z^2 + 32354400 z^3 - 24995100 z^4 + 7210125 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])

Standard Form

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MathML Form

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type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 7210125 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24995100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32354400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18918960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4685168 </cn> <ci> z </ci> 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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,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]