Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9303)

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=-7/4

http://functions.wolfram.com/07.23.03.9303.01

Input Form

Hypergeometric2F1[-(23/4), -(7/4), 11/2, z] == (1/(8863231216125 Pi^(3/2) z^(9/2))) (32 (2 (-11306064 + 205528092 z - 1984786265 z^2 + 15422346170 z^3 - 182666120175 z^4 - 921458186968 z^5 - 592554275591 z^6 - 19486770030 z^7 + 1890998655 z^8 - 173387760 z^9 + 8910720 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-11306064 + 205528092 z - 1984786265 z^2 + 15422346170 z^3 - 182666120175 z^4 - 921458186968 z^5 - 592554275591 z^6 - 19486770030 z^7 + 1890998655 z^8 - 173387760 z^9 + 8910720 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (-11306064 - 5653032 Sqrt[z] + 205528092 z + 102292960 z^(3/2) - 1984786265 z^2 - 984065005 z^(5/2) + 15422346170 z^3 + 7632602670 z^(7/2) - 182666120175 z^4 - 367705120915 z^(9/2) - 921458186968 z^5 - 940161911804 z^(11/2) - 592554275591 z^6 - 400105599075 z^(13/2) - 19486770030 z^7 + 460897710 z^(15/2) + 1890998655 z^8 - 42720405 z^(17/2) - 173387760 z^9 + 2227680 z^(19/2) + 8910720 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (-11306064 + 5653032 Sqrt[z] + 205528092 z - 102292960 z^(3/2) - 1984786265 z^2 + 984065005 z^(5/2) + 15422346170 z^3 - 7632602670 z^(7/2) - 182666120175 z^4 + 367705120915 z^(9/2) - 921458186968 z^5 + 940161911804 z^(11/2) - 592554275591 z^6 + 400105599075 z^(13/2) - 19486770030 z^7 - 460897710 z^(15/2) + 1890998655 z^8 + 42720405 z^(17/2) - 173387760 z^9 - 2227680 z^(19/2) + 8910720 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML 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]