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

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=-9/4, b>=a

For fixed z and a=-9/4, b=15/4

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

Input Form

Hypergeometric2F1[-(9/4), 15/4, -(11/2), z] == (1/(4553472 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-1138368 + 6079920 z - 12129656 z^2 + 9827279 z^3 - 945945 z^4 - 791791 z^5 - 2277275 z^6 + 4435548 z^7 - 2609152 z^8 + 532480 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-1138368 + 6079920 z - 12129656 z^2 + 9827279 z^3 - 945945 z^4 - 791791 z^5 - 2277275 z^6 + 4435548 z^7 - 2609152 z^8 + 532480 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((1138368 - 569184 Sqrt[z] - 5510736 z + 2518208 z^(3/2) + 9611448 z^2 - 3776234 z^(5/2) - 6051045 z^3 + 1531530 z^(7/2) - 585585 z^4 + 830830 z^(9/2) - 39039 z^5 + 382382 z^(11/2) + 1894893 z^6 - 2840604 z^(13/2) - 1594944 z^7 + 2209792 z^(15/2) + 399360 z^8 - 532480 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((-1138368 - 569184 Sqrt[z] + 5510736 z + 2518208 z^(3/2) - 9611448 z^2 - 3776234 z^(5/2) + 6051045 z^3 + 1531530 z^(7/2) + 585585 z^4 + 830830 z^(9/2) + 39039 z^5 + 382382 z^(11/2) - 1894893 z^6 - 2840604 z^(13/2) + 1594944 z^7 + 2209792 z^(15/2) - 399360 z^8 - 532480 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 2609152 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4435548 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2277275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 791791 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 945945 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9827279 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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]