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%I #20 Feb 27 2021 13:20:38
%S 3,3,9,2,7,6,4,2,7,8,9,2,7,8,4,9,8,0,7,7,0,4,7,5,5,0,5,6,5,5,4,4,7,1,
%T 2,8,3,9,2,7,4,0,1,0,9,2,5,8,6,0,8,4,4,2,2,3,4,7,8,0,8,4,4,1,9,3,5,2,
%U 4,6,3,6,1,5,9,8,0,3,4,6,1,3,5,1,7,3,5,0,1,0,5,1,9,3,2,9,7,8,5,7,3,4,6,7,3
%N Decimal expansion of the constant 5*exp(psi(4/5) + 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="/A097670/b097670.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 = ((sqrt(5)+1)/2)^(-sqrt(5)/2)/5^(1/4)*exp(Pi/2*sqrt(1+2/sqrt(5))).
%e c = 3.39276427892784980770475505655447128392740109258608442234780...
%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(4/5)+Euler)
%Y Cf. A097663-A097669, A097671-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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