Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4655)

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=-17/3, b>=a

For fixed z and a=-17/3, b=-4/3

http://functions.wolfram.com/07.23.03.4655.01

Input Form

Hypergeometric2F1[-(17/3), -(4/3), 11/2, z] == (6561 (Sqrt[z] (-2654208 + 45907968 z - 413990912 z^2 + 2906849280 z^3 + 116353637477 z^4 + 1257424327 z^5 - 116387108172 z^6 - 4268223712 z^7 + 565189120 z^8 - 60446208 z^9 + 3415040 z^10) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (7962624 - 135364608 z + 1202913280 z^2 - 8381333504 z^3 + 84885143552 z^4 + 425795160439 z^5 + 233797090492 z^6 - 4007229280 z^7 + 536246656 z^8 - 58738688 z^9 + 3415040 z^10) Sin[ArcSin[Sqrt[z]]/3]))/(954146869000325 Sqrt[1 - z] z^(9/2))

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]