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

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=17/4

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

Input Form

Hypergeometric2F1[-(13/4), 17/4, 6, z] == (1/(333107775 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((-(-2048 - 2048 Sqrt[z] + 2784 z + 2784 z^(3/2) + 1341 z^2 + 1341 z^(5/2) + 1606 z^3 + 1606 z^(7/2) + 4125 z^4 + 4125 z^(9/2) - 88704 z^5 - 88704 z^(11/2) + 167552 z^6 + 167552 z^(13/2) - 118272 z^7 - 118272 z^(15/2) + 29568 z^8 + 29568 z^(17/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-2048 + 3296 z + 789 z^2 + 1153 z^3 + 3575 z^4 - 49269 z^5 + 88088 z^6 - 60368 z^7 + 14784 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]