Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7953)

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=11/3

http://functions.wolfram.com/07.23.03.7953.01

Input Form

Hypergeometric2F1[4/3, 11/3, -(9/2), -z] == (1/(1679616 (1 + z)^(19/2))) ((1679616 + 17874432 z + 88945920 z^2 + 281910272 z^3 + 690606592 z^4 + 2100798464 z^5 - 2286882049 z^6 - 32429540 z^7 - 1995664 z^8) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (559872 + 5564160 z + 25776128 z^2 + 76237824 z^3 + 178338304 z^4 - 1139624707 z^5 + 31431708 z^6 + 1995664 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]