Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4pt)

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=-33/8

http://functions.wolfram.com/07.23.03.b4pt.01

Input Form

Hypergeometric2F1[-(47/8), -(33/8), 11/2, z] == (1/(2789675218916841 z^(9/2))) (1024 (-2 Sqrt[z] (-326368 + 8293244 z - 118015543 z^2 + 1452838808 z^3 - 1392434153108 z^4 - 6323884359296 z^5 - 7669307649754 z^6 - 2944605766008 z^7 - 305002736724 z^8 - 2539314588 z^9 + 31221081 z^10) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((2610944 - 68140976 z + 989523007 z^2 - 12266456774 z^3 + 250220127124 z^4 + 2069221599824 z^5 + 1907327408778 z^6 - 1973736075548 z^7 - 1922088383052 z^8 - 314554805232 z^9 - 5109850257 z^10 + 62442162 z^11) Sin[ArcSin[Sqrt[z]]/4])))

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]