Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.an29)

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=17/4

http://functions.wolfram.com/07.23.03.an29.01

Input Form

Hypergeometric2F1[17/4, 17/4, -(3/2), z] == (1/(91260 Pi^(3/2))) ((-((1/(-1 + z)^10) (4 Sqrt[z] (-22815 + 494325 z + 201134946 z^2 + 556707666 z^3 + 277805309 z^4 + 20845177 z^5) EllipticE[(1/2) (1 - Sqrt[z])])) + (1/(-1 + z)^10) (4 Sqrt[z] (-22815 + 494325 z + 201134946 z^2 + 556707666 z^3 + 277805309 z^4 + 20845177 z^5) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((91260 - 136890 Sqrt[z] - 1908855 z + 2897505 z^(3/2) + 43226820 z^2 + 359043072 z^(5/2) + 262039974 z^3 + 851375358 z^(7/2) + 203027416 z^4 + 352583202 z^(9/2) + 22005689 z^5 + 19684665 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((-91260 - 136890 Sqrt[z] + 1908855 z + 2897505 z^(3/2) - 43226820 z^2 + 359043072 z^(5/2) - 262039974 z^3 + 851375358 z^(7/2) - 203027416 z^4 + 352583202 z^(9/2) - 22005689 z^5 + 19684665 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 262039974 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 359043072 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 43226820 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2897505 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1908855 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 136890 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 91260 </cn> </apply> <apply> <ci> EllipticK </ci> <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,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]