Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab68)

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=-7/4

http://functions.wolfram.com/07.23.03.ab68.01

Input Form

Hypergeometric2F1[-(15/4), -(7/4), 9/2, z] == (1/(318687525 Pi^(3/2) z^(7/2))) (16 (8 (2310 - 34881 z + 307153 z^2 - 3505425 z^3 - 14870180 z^4 - 6944135 z^5 - 125307 z^6 + 4641 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 8 (2310 - 34881 z + 307153 z^2 - 3505425 z^3 - 14870180 z^4 - 6944135 z^5 - 125307 z^6 + 4641 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (9240 + 4620 Sqrt[z] - 139524 z - 69377 z^(3/2) + 1228612 z^2 + 608685 z^(5/2) - 14021700 z^3 - 26880410 z^(7/2) - 59480720 z^4 - 56858090 z^(9/2) - 27776540 z^5 - 17473365 z^(11/2) - 501228 z^6 + 4641 z^(13/2) + 18564 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (9240 - 4620 Sqrt[z] - 139524 z + 69377 z^(3/2) + 1228612 z^2 - 608685 z^(5/2) - 14021700 z^3 + 26880410 z^(7/2) - 59480720 z^4 + 56858090 z^(9/2) - 27776540 z^5 + 17473365 z^(11/2) - 501228 z^6 - 4641 z^(13/2) + 18564 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 59480720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26880410 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14021700 </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'> 608685 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1228612 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69377 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </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]