Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7229)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-2/3, b>=a

For fixed z and a=-2/3, b=17/3

http://functions.wolfram.com/07.23.03.7229.01

Input Form

Hypergeometric2F1[-(2/3), 17/3, -(11/2), z] == ((1/Sqrt[1 - z]) ((387991296 - 3828964608 z + 16691560704 z^2 - 41632490240 z^3 + 63061542400 z^4 - 51414454784 z^5 - 14751948288 z^6 + 21514834041 z^7 - 15026533512 z^8 + 6226108832 z^9 - 1462277440 z^10 + 150944768 z^11) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (129330432 - 1185311232 z + 4739680512 z^2 - 10628382720 z^3 + 13864040960 z^4 - 8046517248 z^5 + 15920670357 z^6 - 12414662896 z^7 + 5551574400 z^8 - 1386805056 z^9 + 150944768 z^10) Sin[ArcSin[Sqrt[z]]/3])/(387991296 (-1 + z)^10)

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]