Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7r7)

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=19/4

http://functions.wolfram.com/07.23.03.a7r7.01

Input Form

Hypergeometric2F1[-(23/4), 19/4, 4, z] == -((1/(4928737275 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((13984 + 109687 z + 1162420 z^2 - 34633725 z^3 + 157874850 z^4 - 311268048 z^5 + 313194336 z^6 - 158695680 z^7 + 32248320 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-13984 + 13984 Sqrt[z] - 120175 z + 120175 z^(3/2) - 1254190 z^2 + 1254190 z^(5/2) - 4827375 z^3 + 4827375 z^(7/2) + 98867580 z^4 - 98867580 z^(9/2) - 317592912 z^5 + 317592912 z^(11/2) + 429461760 z^6 - 429461760 z^(13/2) - 269018880 z^7 + 269018880 z^(15/2) + 64496640 z^8 - 64496640 z^(17/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]