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%I #23 Sep 08 2022 08:45:14
%S 1,4,2,9,8,8,4,3,0,8,4,0,1,2,3,4,2,0,5,6,6,1,7,9,0,4,2,4,7,7,5,1,3,8,
%T 0,9,6,5,6,4,9,8,2,3,6,7,6,7,5,6,4,4,6,4,8,8,7,6,3,4,6,2,1,4,8,8,3,6,
%U 9,9,4,5,0,9,1,2,2,0,3,9,6,1,6,1,8,2,1,9,5,9,1,4,6,9,0,1,8,4,6,3,6,2,3,7,8
%N Decimal expansion of the constant 3*exp(psi(2/3) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.
%C This constant appears in _Benoit Cloitre_'s generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-3 linear recursions with varying coefficients (see A097678 for example).
%D A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
%H G. C. Greubel, <a href="/A097664/b097664.txt">Table of n, a(n) for n = 1..2500</a>
%H Benoit Cloitre, <a href="/A097679/a097679.pdf">On a generalization of Euler-Gauss formula for the Gamma function</a>, preprint 2004.
%H Andrew Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf">Asymptotic enumeration methods</a>, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.
%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma Function</a>.
%F c = 1/sqrt(3)*exp(Pi/sqrt(12)).
%e c = 1.42988430840123420566179042477513809656498236767564464887634...
%t RealDigits[1/Sqrt[3]*E^(Pi/Sqrt[12]), 10, 105][[1]] (* _Robert G. Wilson v_, Aug 28 2004 *)
%o (PARI) 3*exp(psi(2/3)+Euler)
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (1/Sqrt(3))*Exp(Pi(R)/Sqrt(12)); // _G. C. Greubel_, Aug 27 2018
%Y Cf. A097663, A097665-A097676.
%K cons,nonn
%O 1,2
%A _Paul D. Hanna_, Aug 25 2004
%E More terms from _Robert G. Wilson v_, Aug 28 2004
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