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

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=17/4

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

Input Form

Hypergeometric2F1[-(15/4), 17/4, -(11/2), z] == (1/(411840 Pi^(3/2))) (((1/(-1 + z)^6) (4 Sqrt[z] (102960 - 280800 z + 136773 z^2 + 73983 z^3 + 66339 z^4 + 94185 z^5 - 3484320 z^6 + 6129408 z^7 - 3981312 z^8 + 917504 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^6) (4 Sqrt[z] (102960 - 280800 z + 136773 z^2 + 73983 z^3 + 66339 z^4 + 94185 z^5 - 3484320 z^6 + 6129408 z^7 - 3981312 z^8 + 917504 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((411840 - 617760 Sqrt[z] - 814320 z + 1375920 z^(3/2) - 32760 z^2 - 240786 z^(5/2) + 229593 z^3 - 377559 z^(7/2) + 407862 z^4 - 540540 z^(9/2) + 683865 z^5 - 872235 z^(11/2) + 2009280 z^6 + 4959360 z^(13/2) - 7534080 z^7 - 4724736 z^(15/2) + 6586368 z^8 + 1376256 z^(17/2) - 1835008 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-411840 - 617760 Sqrt[z] + 814320 z + 1375920 z^(3/2) + 32760 z^2 - 240786 z^(5/2) - 229593 z^3 - 377559 z^(7/2) - 407862 z^4 - 540540 z^(9/2) - 683865 z^5 - 872235 z^(11/2) - 2009280 z^6 + 4959360 z^(13/2) + 7534080 z^7 - 4724736 z^(15/2) - 6586368 z^8 + 1376256 z^(17/2) + 1835008 z^9) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

Standard Form

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MathML Form

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<times /> <cn type='integer'> 377559 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 229593 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 240786 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1375920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 814320 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 617760 </cn> <apply> <power /> <ci> z </ci> <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]