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

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=15/4, b>=a

For fixed z and a=15/4, b=19/4

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

Input Form

Hypergeometric2F1[15/4, 19/4, -(3/2), z] == (1/(40656 Pi^(3/2))) (((1/(-1 + z)^10) (2 (10164 - 221067 z + 4933775 z^2 + 41479970 z^3 + 45729570 z^4 + 8679833 z^5 + 51051 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^10) (2 (10164 - 221067 z + 4933775 z^2 + 41479970 z^3 + 45729570 z^4 + 8679833 z^5 + 51051 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((10164 - 5082 Sqrt[z] - 215985 z + 105875 z^(3/2) + 4827900 z^2 + 7245560 z^(5/2) + 34234410 z^3 + 13836330 z^(7/2) + 31893240 z^4 + 3932090 z^(9/2) + 4747743 z^5 + 51051 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((10164 + 5082 Sqrt[z] - 215985 z - 105875 z^(3/2) + 4827900 z^2 - 7245560 z^(5/2) + 34234410 z^3 - 13836330 z^(7/2) + 31893240 z^4 - 3932090 z^(9/2) + 4747743 z^5 - 51051 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

Standard Form

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MathML Form

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-1 </cn> <apply> <times /> <cn type='integer'> 5082 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 10164 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 10 </cn> </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]