Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8637)

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=10/3, b>=a

For fixed z and a=10/3, b=17/3

http://functions.wolfram.com/07.23.03.8637.01

Input Form

Hypergeometric2F1[10/3, 17/3, -(3/2), -z] == (1/(6193152 (1 + z)^(21/2))) ((6193152 + 143360000 z + 3388571648 z^2 - 35650476899 z^3 + 49376833176 z^4 - 12209386096 z^5 - 72569600 z^6 - 2902784 z^7) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (2064384 + 46333952 z - 7429771817 z^2 + 18613085216 z^3 - 7317469360 z^4 + 71118208 z^5 + 2902784 z^6) 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]