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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-19/8

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

Input Form

Hypergeometric2F1[-(37/8), -(19/8), 5/2, -z] == -((1/(1826331675 z^(3/2) Sqrt[1 + z])) (16 (Sqrt[z] Sqrt[1 + z] (-795093 - 151829825 z + 1028257706 z^2 - 1204366706 z^3 + 229282975 z^4 + 6190979 z^5 + 270940 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (1060124 + 51150983 z - 616619325 z^2 + 352310938 z^3 + 792732034 z^4 - 232344597 z^5 - 6326449 z^6 - 270940 z^7) Sinh[(3 ArcSinh[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]