Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb8b)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-37/8, b>=a

For fixed z and a=-37/8, b=-33/8

http://functions.wolfram.com/07.23.03.bb8b.01

Input Form

Hypergeometric2F1[-(37/8), -(33/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (2988605440 - 65387418240 z + 761411717775 z^2 - 6882198420825 z^3 + 69884796529275 z^4 + 4359413116603587 z^5 + 11848643809662093 z^6 + 8402445223150965 z^7 + 1680948517886505 z^8 + 67812383709665 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (2988605440 - 65387418240 z + 761411717775 z^2 - 6882198420825 z^3 + 69884796529275 z^4 + 4359413116603587 z^5 + 11848643809662093 z^6 + 8402445223150965 z^7 + 1680948517886505 z^8 + 67812383709665 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (2988605440 - 65387418240 z + 761411717775 z^2 - 6882198420825 z^3 + 69884796529275 z^4 + 4359413116603587 z^5 + 11848643809662093 z^6 + 8402445223150965 z^7 + 1680948517886505 z^8 + 67812383709665 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-2988605440 + 66508145280 z - 785625550815 z^2 + 7161185851350 z^3 - 72391001851350 z^4 - 1086626303282562 z^5 - 947321051585076 z^6 + 1120966351503138 z^7 + 868113970519110 z^8 + 109395310836490 z^9 + 1423644019875 z^10) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (851246182692307727325 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)

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]