Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4703)

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=2/3

http://functions.wolfram.com/07.23.03.4703.01

Input Form

Hypergeometric2F1[-(17/3), 2/3, 11/2, z] == (6561 (Sqrt[z] (-1161216 + 13338624 z - 71559168 z^2 + 245463040 z^3 + 265058453 z^4 - 762300477 z^5 + 474108016 z^6 - 221081704 z^7 + 70649376 z^8 - 13739648 z^9 + 1224704 z^10) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (3483648 - 38983680 z + 203585536 z^2 - 680929280 z^3 + 2035855360 z^4 - 589529721 z^5 + 386101920 z^6 - 190526664 z^7 + 64238816 z^8 - 13127296 z^9 + 1224704 z^10) Sin[ArcSin[Sqrt[z]]/3]))/ (6580323234485 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]