Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4v7)

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=-17/8

http://functions.wolfram.com/07.23.03.b4v7.01

Input Form

Hypergeometric2F1[-(47/8), -(17/8), 9/2, z] == (1/(25730311907025 z^(7/2))) (256 ((-Sqrt[z]) (536176 - 11226185 z + 144298366 z^2 - 103089628303 z^3 - 297875610612 z^4 - 158220400959 z^5 - 5912369490 z^6 + 465715263 z^7 - 39838344 z^8 + 1982904 z^9) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) (4 (-536176 + 11594806 z - 151972385 z^2 + 2678902851 z^3 + 14129185937 z^4 - 1779453009 z^5 - 13464264129 z^6 - 1535092815 z^7 + 121346643 z^8 - 10207449 z^9 + 495726 z^10) 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]