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%I #20 Feb 27 2021 13:20:38
%S 0,0,3,2,4,1,1,2,2,8,3,0,0,9,6,3,0,7,3,7,4,7,5,1,1,7,1,2,1,7,9,1,9,0,
%T 1,7,0,1,0,7,3,8,4,7,9,2,2,1,5,1,0,4,0,0,6,9,2,9,9,0,5,9,2,3,0,5,1,8,
%U 5,7,1,1,0,2,1,3,7,4,1,0,1,1,3,2,7,9,8,7,0,4,4,4,3,6,4,9,4,7,3,7,7,4,7,2,2
%N Decimal expansion of the constant 8*exp(psi(1/8) + 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-8 linear recursions with varying coefficients (see A097682 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="/A097673/b097673.txt">Table of n, a(n) for n = 0..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 Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma Function</a>.
%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.
%F c = (1+sqrt(2))^(-sqrt(2))/2*exp(-Pi/2*(1+sqrt(2))).
%e c = 0.00324112283009630737475117121791901701073847922151040069299...
%t RealDigits[(1 + Sqrt[2])^(-Sqrt[2])/2E^(-Pi/2*(1 + Sqrt[2])), 10, 103][[1]] (* _Robert G. Wilson v_, Aug 27 2004 *)
%o (PARI) 8*exp(psi(1/8)+Euler)
%Y Cf. A097663-A097672, A097674-A097676.
%K cons,nonn
%O 0,3
%A _Paul D. Hanna_, Aug 25 2004
%E More terms from _Robert G. Wilson v_, Aug 27 2004
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