Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9bu)

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=-1/4

http://functions.wolfram.com/07.23.03.a9bu.01

Input Form

Hypergeometric2F1[-(19/4), -(1/4), 3, z] == (1/(40883535 Pi Sqrt[1 + Sqrt[z]] z^2)) (64 (-4 (1463 + 1463 Sqrt[z] - 21945 z - 21945 z^(3/2) - 422880 z^2 - 422880 z^(5/2) - 21378 z^3 - 21378 z^(7/2) + 7623 z^4 + 7623 z^(9/2) - 1845 z^5 - 1845 z^(11/2) + 210 z^6 + 210 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (5852 - 89243 z - 392376 z^2 + 609486 z^3 - 184704 z^4 + 64485 z^5 - 15180 z^6 + 1680 z^7) 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]