Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a994)

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=-5/4

http://functions.wolfram.com/07.23.03.a994.01

Input Form

Hypergeometric2F1[-(19/4), -(5/4), 2, z] == (1/(1514205 Pi Sqrt[1 + Sqrt[z]] z)) (8 ((7315 + 7315 Sqrt[z] + 620832 z + 620832 z^(3/2) + 1191426 z^2 + 1191426 z^(5/2) + 18300 z^3 + 18300 z^(7/2) - 3165 z^4 - 3165 z^(9/2) + 300 z^5 + 300 z^(11/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-7315 - 240452 z + 17142 z^2 + 262860 z^3 - 38115 z^4 + 6480 z^5 - 600 z^6) 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]