Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a94a)

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=-13/4

http://functions.wolfram.com/07.23.03.a94a.01

Input Form

Hypergeometric2F1[-(19/4), -(13/4), 4, z] == (1/(155607276825 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((86944 - 2089373 z + 36924030 z^2 + 1971447645 z^3 + 5690452740 z^4 + 3639379437 z^5 + 474743166 z^6 + 215475 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-86944 + 86944 Sqrt[z] + 2024165 z - 2024165 z^(3/2) - 35416095 z^2 + 35416095 z^(5/2) - 782094480 z^3 + 782094480 z^(7/2) - 1513334670 z^4 + 1513334670 z^(9/2) - 593069067 z^5 + 593069067 z^(11/2) - 31243875 z^6 + 31243875 z^(13/2) + 430950 z^7 - 430950 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]