Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9wm)

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=23/4

http://functions.wolfram.com/07.23.03.a9wm.01

Input Form

Hypergeometric2F1[-(19/4), 23/4, 2, z] == (1/(168245 Pi z)) (8 Sqrt[1 + Sqrt[z]] ((-385 + 47154 z - 422032 z^2 + 1224288 z^3 - 1414400 z^4 + 565760 z^5) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (385 - 385 Sqrt[z] - 4804 z + 4804 z^(3/2) - 153296 z^2 + 153296 z^(5/2) + 1048320 z^3 - 1048320 z^(7/2) - 1980160 z^4 + 1980160 z^(9/2) + 1131520 z^5 - 1131520 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]