Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9393)

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=-3/4

http://functions.wolfram.com/07.23.03.9393.01

Input Form

Hypergeometric2F1[-(23/4), -(3/4), 11/2, z] == (1/(1772646243225 Pi^(3/2) z^(9/2))) (32 (-2 (8075760 - 123155340 z + 961250983 z^2 - 5702496030 z^3 + 46774527921 z^4 + 126153295136 z^5 + 10912141305 z^6 - 2189741814 z^7 + 428685855 z^8 - 59256288 z^9 + 4073472 z^10) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (8075760 - 123155340 z + 961250983 z^2 - 5702496030 z^3 + 46774527921 z^4 + 126153295136 z^5 + 10912141305 z^6 - 2189741814 z^7 + 428685855 z^8 - 59256288 z^9 + 4073472 z^10) EllipticE[(1/2) (1 + Sqrt[z])] + (8075760 + 4037880 Sqrt[z] - 123155340 z - 61241180 z^(3/2) + 961250983 z^2 + 475662264 z^(5/2) - 5702496030 z^3 - 2813652468 z^(7/2) + 46774527921 z^4 + 78563296064 z^(9/2) + 126153295136 z^5 + 101429094780 z^(11/2) + 10912141305 z^6 - 519447240 z^(13/2) - 2189741814 z^7 + 103160148 z^(15/2) + 428685855 z^8 - 14527656 z^(17/2) - 59256288 z^9 + 1018368 z^(19/2) + 4073472 z^10) EllipticK[(1/2) (1 - Sqrt[z])] - (8075760 - 4037880 Sqrt[z] - 123155340 z + 61241180 z^(3/2) + 961250983 z^2 - 475662264 z^(5/2) - 5702496030 z^3 + 2813652468 z^(7/2) + 46774527921 z^4 - 78563296064 z^(9/2) + 126153295136 z^5 - 101429094780 z^(11/2) + 10912141305 z^6 + 519447240 z^(13/2) - 2189741814 z^7 - 103160148 z^(15/2) + 428685855 z^8 + 14527656 z^(17/2) - 59256288 z^9 - 1018368 z^(19/2) + 4073472 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]