Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5721)

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=-11/3, b>=a

For fixed z and a=-11/3, b=-1/3

http://functions.wolfram.com/07.23.03.5721.01

Input Form

Hypergeometric2F1[-(11/3), -(1/3), 9/2, z] == -((243 (Sqrt[z] (-69120 + 783872 z - 4681728 z^2 - 68614527 z^3 + 67034777 z^4 + 6481998 z^5 - 1022856 z^6 + 87584 z^7) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (207360 - 2290176 z + 13393920 z^2 - 84502528 z^3 - 173726165 z^4 + 6003414 z^5 - 979064 z^6 + 87584 z^7) Sin[ArcSin[Sqrt[z]]/3]))/ (23816371085 Sqrt[1 - z] z^(7/2)))

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]