Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a96k)

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=-9/4

http://functions.wolfram.com/07.23.03.a96k.01

Input Form

Hypergeometric2F1[-(19/4), -(9/4), 2, z] == (1/(19684665 Pi z)) (8 Sqrt[1 + Sqrt[z]] ((65835 + 8612126 z + 32637786 z^2 + 17345424 z^3 + 62595 z^4 - 3510 z^5) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-65835 + 65835 Sqrt[z] - 3740336 z + 3740336 z^(3/2) - 8845698 z^2 + 8845698 z^(5/2) - 2141100 z^3 + 2141100 z^(7/2) + 119925 z^4 - 119925 z^(9/2) - 7020 z^5 + 7020 z^(11/2)) 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]