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%I #6 Sep 14 2019 06:37:00
%S 8,4,3,3,0,2,1,0,7,5,3,1,9,7,7,9,6,4,0,9,6,9,9,6,8,1,7,1,5,4,7,6,8,6,
%T 8,3,3,8,3,5,7,4,9,2,4,2,5,2,9,2,5,6,1,6,7,3,0,6,5,1,6,0,5,1,4,8,4,2,
%U 6,1,2,9,0,7,9,2,0,4,3,6,3,8,5,9,0,8,0
%N Decimal expansion of Sum_{k>=1} 1/k + exp(k) * Ei(-k), where Ei(x) is the exponential integral of the first kind.
%C This constant is introduced in the paper by Sampedro.
%H Juan Carlos Sampedro, <a href="https://doi.org/10.1007/s11139-017-9912-7">On a new constant related to Euler's constant</a>, The Ramanujan Journal, Vol. 46, No. 1 (2018), pp. 77-89.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.
%F Equals Integral_{x=0..oo} log(Gamma(x)) * exp(-x) dx. See the paper by Sampedro for other formulas.
%e 0.843302107531977964096996817154768683383574924252925...
%t RealDigits[N[Integrate[Exp[-x]*Log[Gamma[x]], {x, 0, Infinity}], 100], 10, 100][[1]]
%Y Cf. A001620.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Sep 14 2019
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