Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9em)

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=3/4

http://functions.wolfram.com/07.23.03.a9em.01

Input Form

Hypergeometric2F1[-(19/4), 3/4, 4, z] == (1/(422463195 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((46816 + 46816 Sqrt[z] - 399399 z - 399399 z^(3/2) + 1650264 z^2 + 1650264 z^(5/2) + 1037046 z^3 + 1037046 z^(7/2) - 801180 z^4 - 801180 z^(9/2) + 404361 z^5 + 404361 z^(11/2) - 118020 z^6 - 118020 z^(13/2) + 15120 z^7 + 15120 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (46816 - 411103 z + 1746822 z^2 - 2649714 z^3 + 2395896 z^4 - 1779687 z^5 + 864330 z^6 - 243600 z^7 + 30240 z^8) 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]