Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4v8)

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.b4v8.01

Input Form

Hypergeometric2F1[-(47/8), -(17/8), 9/2, -z] == (256 ((-Sqrt[z]) Sqrt[1 + 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) Cosh[ArcSinh[Sqrt[z]]/4] + 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) Sinh[ArcSinh[Sqrt[z]]/4]))/(25730311907025 z^(7/2) Sqrt[1 + z])

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]