Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.acl4)

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=-13/4, b>=a

For fixed z and a=-13/4, b=9/4

http://functions.wolfram.com/07.23.03.acl4.01

Input Form

Hypergeometric2F1[-(13/4), 9/4, 5, z] == (1/(353296125 Pi Sqrt[1 + Sqrt[z]] z^4)) (4096 (-2 (7488 + 7488 Sqrt[z] - 30264 z - 30264 z^(3/2) + 31941 z^2 + 31941 z^(5/2) + 20475 z^3 + 20475 z^(7/2) - 173285 z^4 - 173285 z^(9/2) + 210189 z^5 + 210189 z^(11/2) - 108192 z^6 - 108192 z^(13/2) + 21168 z^7 + 21168 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (14976 - 64272 z + 77961 z^2 + 28665 z^3 - 186865 z^4 + 218323 z^5 - 109956 z^6 + 21168 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]