Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9482)

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/07.23.03.9482.01

Input Form

Hypergeometric2F1[-(23/4), 1/4, 5, z] == (1/(192220753725 Pi z^4)) (4096 (-4 Sqrt[1 - z] (27968 - 325128 z + 1870797 z^2 - 8253182 z^3 - 14255850 z^4 + 7209048 z^5 - 3272843 z^6 + 1072662 z^7 - 218112 z^8 + 20480 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (55936 - 692208 z + 4225353 z^2 - 19268641 z^3 + 77482650 z^4 + 4003566 z^5 - 1774003 z^6 + 565683 z^7 - 111936 z^8 + 10240 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 2 Sqrt[1 - z] (27968 - 325128 z + 1870797 z^2 - 8253182 z^3 - 14255850 z^4 + 7209048 z^5 - 3272843 z^6 + 1072662 z^7 - 218112 z^8 + 20480 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

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]