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A097672 Decimal expansion of the constant 6*exp(psi(5/6) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 3

%I #19 Feb 27 2021 13:20:38

%S 4,3,8,5,2,4,5,9,8,6,2,5,0,8,0,8,1,7,3,6,9,9,4,8,9,9,4,3,2,2,9,5,6,2,

%T 0,7,7,6,5,0,8,0,1,2,8,5,0,0,9,0,2,7,6,3,0,4,2,0,0,6,5,5,4,6,7,7,6,4,

%U 3,3,1,5,6,4,6,0,8,4,8,1,1,5,4,4,3,9,9,7,3,9,5,5,1,5,6,0,8,7,7,8,8,4,6,6,7

%N Decimal expansion of the constant 6*exp(psi(5/6) + 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-6 linear recursions with varying coefficients (see A097681 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="/A097672/b097672.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 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(12)*exp(Pi/2*sqrt(3)).

%e c = 4.38524598625080817369948994322956207765080128500902763042006...

%t RealDigits[1/Sqrt[12]*E^(Pi/2Sqrt[3]), 10, 105][[1]] (* _Robert G. Wilson v_, Aug 27 2004 *)

%o (PARI) 6*exp(psi(5/6)+Euler)

%Y Cf. A097663-A097671, A097673-A097676.

%K cons,nonn

%O 1,1

%A _Paul D. Hanna_, Aug 25 2004

%E More terms from _Robert G. Wilson v_, Aug 27 2004

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