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

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=-17/4, b>=a

For fixed z and a=-17/4, b=21/4

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

Input Form

Hypergeometric2F1[-(17/4), 21/4, 4, z] == (1/(10094175 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((-32 - 32 Sqrt[z] - 267 z - 267 z^(3/2) - 2703 z^2 - 2703 z^(5/2) + 191530 z^3 + 191530 z^(7/2) - 905520 z^4 - 905520 z^(9/2) + 1604064 z^5 + 1604064 z^(11/2) - 1241856 z^6 - 1241856 z^(13/2) + 354816 z^7 + 354816 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (-32 - 259 z - 2634 z^2 + 113365 z^3 - 498520 z^4 + 846384 z^5 - 635712 z^6 + 177408 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]