Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4mk)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-43/8

http://functions.wolfram.com/07.23.03.b4mk.01

Input Form

Hypergeometric2F1[-(47/8), -(43/8), 11/2, -z] == (1024 (Sqrt[z] (448 + 13016 z + 215407 z^2 + 3152072 z^3 + 1760766228 z^4 - 10722331256 z^5 + 18671958602 z^6 - 11658625160 z^7 + 2577610676 z^8 - 163058976 z^9 + 1295679 z^10) Cos[ArcTan[Sqrt[z]]/4] - (1792 + 52624 z + 877751 z^2 + 12873352 z^3 + 325501652 z^4 - 5249073544 z^5 + 16182949978 z^6 - 16720584328 z^7 + 6287663860 z^8 - 777730184 z^9 + 21240231 z^10) Sin[ArcTan[Sqrt[z]]/4]))/ (1720687317085 z^(9/2) (1 + z)^(1/8))

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]