Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5816)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-11/3, b>=a

For fixed z and a=-11/3, b=8/3

http://functions.wolfram.com/07.23.03.5816.01

Input Form

Hypergeometric2F1[-(11/3), 8/3, -(11/2), -z] == (1/19683) ((1/(1 + z)^(9/2)) ((19683 + 54675 z + 38178 z^2 - 2282 z^3 + 1655 z^4 - 2249 z^5 + 8180 z^6 + 16432 z^7 + 6656 z^8) Cosh[ArcSinh[Sqrt[z]]/3]) + (1/(1 + z)^4) (Sqrt[z] (-6561 - 13608 z - 3654 z^2 + 2532 z^3 - 2257 z^4 + 2460 z^5 + 13104 z^6 + 6656 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))

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]