Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9532)

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=-23/4, b>=a

For fixed z and a=-23/4, b=3/4

http://functions.wolfram.com/07.23.03.9532.01

Input Form

Hypergeometric2F1[-(23/4), 3/4, 3, z] == (1/(140821065 Pi Sqrt[1 + Sqrt[z]] z^2)) (64 (-2 (67298 + 67298 Sqrt[z] - 639331 z - 639331 z^(3/2) - 896184 z^2 - 896184 z^(5/2) + 1120230 z^3 + 1120230 z^(7/2) - 926706 z^4 - 926706 z^(9/2) + 481509 z^5 + 481509 z^(11/2) - 142800 z^6 - 142800 z^(13/2) + 18480 z^7 + 18480 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (134596 - 1312311 z + 2918492 z^2 - 4377738 z^3 + 5220432 z^4 - 4128231 z^5 + 2060520 z^6 - 589680 z^7 + 73920 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]