Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a94e)

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.a94e.01

Input Form

Hypergeometric2F1[-(19/4), -(13/4), 5, z] == (1/(157941385977375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-1043328 + 21866416 z - 263127865 z^2 + 3107894790 z^3 + 120379062825 z^4 + 278364148356 z^5 + 148669284393 z^6 + 16651348710 z^7 + 6248775 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-521664 + 521664 Sqrt[z] + 10541960 z - 10541960 z^(3/2) - 123718595 z^2 + 123718595 z^(5/2) + 1462370910 z^3 - 1462370910 z^(7/2) + 22712354175 z^4 - 22712354175 z^(9/2) + 34918792188 z^5 - 34918792188 z^(11/2) + 11380990635 z^6 - 11380990635 z^(13/2) + 512399550 z^7 - 512399550 z^(15/2) - 6248775 z^8 + 6248775 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]