Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8259)

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=7/3, b>=a

For fixed z and a=7/3, b=8/3

http://functions.wolfram.com/07.23.03.8259.01

Input Form

Hypergeometric2F1[7/3, 8/3, -(11/2), -z] == ((27713664 + 323885952 z + 1771410816 z^2 + 6100984960 z^3 + 15311170304 z^4 + 32697592576 z^5 + 97128934144 z^6 - 131942326177 z^7 + 13861463524 z^8) Cosh[ArcSinh[Sqrt[z]]/3] - 3 Sqrt[z] Sqrt[1 + z] (3079296 + 33820416 z + 173260416 z^2 + 558446080 z^3 + 1320376576 z^4 + 2741064192 z^5 - 19371507617 z^6 + 3338606332 z^7) Sinh[ArcSinh[Sqrt[z]]/3])/(27713664 (1 + z)^(21/2))

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]