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A097668 Decimal expansion of the constant 5*exp(psi(2/5)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 3

%I

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

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

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

%N Decimal expansion of the constant 5*exp(psi(2/5)+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-5 linear recursions with varying coefficients (see A097680 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="/A097668/b097668.txt">Table of n, a(n) for n = 0..2500</a>

%H Benoit Cloitre, <a href="http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/CloitreGammaConstants.pdf">On a generalization of Euler-Gauss formula for the Gamma function</a>, pre-print 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 = ((sqrt(5)+1)/2)^(sqrt(5)/2)/5^(1/4)*exp(-Pi/2*sqrt(1-2/sqrt(5))).

%e c = 0.68747420699080196070816422133398475499777353078320593237327...

%t RealDigits[ GoldenRatio^(Sqrt[5]/2)/5^(1/4)*E^(-Pi/2Sqrt[1 - 2/Sqrt[5]]), 10, 105][[1]] (* _Robert G. Wilson v_, Aug 27 2004 *)

%o (PARI) 5*exp(psi(2/5)+Euler)

%Y Cf. A097663-A097667, A097669-A097676.

%K cons,nonn

%O 0,1

%A _Paul D. Hanna_, Aug 25 2004

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

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