Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6417)

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=-8/3, b>=a

For fixed z and a=-8/3, b=17/3

http://functions.wolfram.com/07.23.03.6417.01

Input Form

Hypergeometric2F1[-(8/3), 17/3, -(7/2), -z] == (1/13608) (-((1/(1 + z)^(13/2)) ((-13608 - 30456 z + 6680 z^2 - 14168 z^3 + 99176 z^4 + 554509 z^5 + 980408 z^6 + 843440 z^7 + 363584 z^8 + 63232 z^9) Cosh[ArcSinh[Sqrt[z]]/3])) - (1/(1 + z)^6) (Sqrt[z] (4536 + 6960 z - 6776 z^2 + 9856 z^3 + 284265 z^4 + 675272 z^5 + 685360 z^6 + 331968 z^7 + 63232 z^8) 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]