Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9485)

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=-23/4, b>=a

For fixed z and a=-23/4, b=1/4

http://functions.wolfram.com/07.23.03.9485.01

Input Form

Hypergeometric2F1[-(23/4), 1/4, 11/2, z] == (1/(1772646243225 Pi^(3/2) z^(9/2))) (32 (2 (-56530320 + 696534300 z - 4146128833 z^2 + 16964917277 z^3 - 77137169494 z^4 - 30634465290 z^5 + 14087374275 z^6 - 5744694111 z^7 + 1700852244 z^8 - 315015168 z^9 + 27156480 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-56530320 + 696534300 z - 4146128833 z^2 + 16964917277 z^3 - 77137169494 z^4 - 30634465290 z^5 + 14087374275 z^6 - 5744694111 z^7 + 1700852244 z^8 - 315015168 z^9 + 27156480 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (-56530320 - 28265160 Sqrt[z] + 696534300 z + 345911720 z^(3/2) - 4146128833 z^2 - 2045219869 z^(5/2) + 16964917277 z^3 + 8323450289 z^(7/2) - 77137169494 z^4 - 93334428330 z^(9/2) - 30634465290 z^5 + 3175232970 z^(11/2) + 14087374275 z^6 - 1327892865 z^(13/2) - 5744694111 z^7 + 404097837 z^(15/2) + 1700852244 z^8 - 76844352 z^(17/2) - 315015168 z^9 + 6789120 z^(19/2) + 27156480 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (-56530320 + 28265160 Sqrt[z] + 696534300 z - 345911720 z^(3/2) - 4146128833 z^2 + 2045219869 z^(5/2) + 16964917277 z^3 - 8323450289 z^(7/2) - 77137169494 z^4 + 93334428330 z^(9/2) - 30634465290 z^5 - 3175232970 z^(11/2) + 14087374275 z^6 + 1327892865 z^(13/2) - 5744694111 z^7 - 404097837 z^(15/2) + 1700852244 z^8 + 76844352 z^(17/2) - 315015168 z^9 - 6789120 z^(19/2) + 27156480 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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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]