A097675 - OEIS

%I #22 Feb 27 2021 13:20:38

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

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

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

%N Decimal expansion of the constant 8*exp(psi(5/8) + 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="/A097675/b097675.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(2))^(sqrt(2))/2*exp(Pi/2*(sqrt(2)-1)).

%e c = 3.33325212658541721540039076972102211743980259727655469662827...

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

%o (PARI) 8*exp(psi(5/8)+Euler)

%Y Cf. A097663-A097674, 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