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A097665 Decimal expansion of the constant 4*exp(psi(1/4) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

%I A097665 #19 Feb 27 2021 13:20:38
%S A097665 1,0,3,9,3,9,7,8,8,1,7,5,3,8,0,9,5,4,2,7,3,4,7,7,8,0,9,9,1,7,4,8,9,3,
%T A097665 8,5,0,1,6,9,3,8,9,2,0,8,1,5,8,8,4,8,0,4,0,3,7,5,6,7,9,4,1,5,2,7,7,0,
%U A097665 9,9,3,8,6,4,2,7,4,1,0,6,9,8,9,4,3,0,0,1,3,8,9,3,2,7,1,3,0,1,7,6,7,0,2,6,0
%N A097665 Decimal expansion of the constant 4*exp(psi(1/4) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.
%C A097665 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-4 linear recursions with varying coefficients (see A097679 for example).
%D A097665 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 A097665 G. C. Greubel, <a href="/A097665/b097665.txt">Table of n, a(n) for n = 0..2500</a>
%H A097665 Benoit Cloitre, <a href="/A097679/a097679.pdf">On a generalization of Euler-Gauss formula for the Gamma function</a>, preprint 2004.
%H A097665 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 A097665 Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma Function</a>.
%F A097665 c = 1/2*exp(-Pi/2).
%e A097665 c = 0.10393978817538095427347780991748938501693892081588480403756...
%t A097665 RealDigits[1/2*E^(-Pi/2), 10, 105][[1]] (* _Robert G. Wilson v_, Aug 28 2004 *)
%o A097665 (PARI) 4*exp(psi(1/4)+Euler)
%Y A097665 Cf. A097663-A097664, A097666-A097676.
%K A097665 cons,nonn
%O A097665 0,3
%A A097665 _Paul D. Hanna_, Aug 25 2004
%E A097665 More terms from _Robert G. Wilson v_, Aug 28 2004