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

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=-17/4, b>=a

For fixed z and a=-17/4, b=7/2

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

Input Form

Hypergeometric2F1[-(17/4), 7/2, 2, z] == (1/(69615 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] (2 (-2652 + 273050 z - 1641393 z^2 + 3390607 z^3 - 2927463 z^4 + 908523 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-2652 + 273050 z - 1641393 z^2 + 3390607 z^3 - 2927463 z^4 + 908523 z^5) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (2652 - 132494 z + 557441 z^2 - 730664 z^3 + 302841 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (2652 - 273050 z + 1641393 z^2 - 3390607 z^3 + 2927463 z^4 - 908523 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (2652 - 273050 z + 1641393 z^2 - 3390607 z^3 + 2927463 z^4 - 908523 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (2652 - 273050 z + 1641393 z^2 - 3390607 z^3 + 2927463 z^4 - 908523 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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -908523 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2927463 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3390607 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1641393 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 273050 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2652 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <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,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]