Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ww)

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=-19/4, b>=a

For fixed z and a=-19/4, b=23/4

http://functions.wolfram.com/07.23.03.a9ww.01

Input Form

Hypergeometric2F1[-(19/4), 23/4, 4, z] == -((1/(140821065 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((224 + 2429 z + 30681 z^2 - 1000134 z^3 + 4439760 z^4 - 7716384 z^5 + 5940480 z^6 - 1697280 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-224 + 224 Sqrt[z] - 2597 z + 2597 z^(3/2) - 32655 z^2 + 32655 z^(5/2) - 124836 z^3 + 124836 z^(7/2) + 2905968 z^4 - 2905968 z^(9/2) - 8686080 z^5 + 8686080 z^(11/2) + 9335040 z^6 - 9335040 z^(13/2) - 3394560 z^7 + 3394560 z^(15/2)) 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]