Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7993)

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=4/3, b>=a

For fixed z and a=4/3, b=14/3

http://functions.wolfram.com/07.23.03.7993.01

Input Form

Hypergeometric2F1[4/3, 14/3, -(9/2), -z] == (1/(3359232 (1 + z)^(21/2))) ((3359232 + 40103424 z + 227243520 z^2 + 836301312 z^3 + 2443037696 z^4 + 9217297408 z^5 - 12925624069 z^6 - 295834510 z^7 - 36375512 z^8 - 2539936 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (1119744 + 12579840 z + 66981376 z^2 + 232556544 z^3 + 655395840 z^4 - 5970168079 z^5 + 278599230 z^6 + 35105544 z^7 + 2539936 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]