Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb9l)

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=-27/8

http://functions.wolfram.com/07.23.03.bb9l.01

Input Form

Hypergeometric2F1[-(37/8), -(27/8), 9/2, -z] == (256 (Sqrt[z] Sqrt[1 + z] (154512 + 3441111 z + 47924472 z^2 + 3238758269 z^3 - 16868078610 z^4 + 19566481233 z^5 - 5959906916 z^6 + 332864763 z^7 + 2211726 z^8) Cosh[(3 ArcSinh[Sqrt[z]])/4] - 2 (103008 + 2382060 z + 33905727 z^2 + 664218117 z^3 - 4994171853 z^4 + 2433269257 z^5 + 5295027725 z^6 - 2599125377 z^7 + 166985313 z^8 + 1105863 z^9) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/ (584513104175 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]