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Decimal expansion of gamma - Ei(-1).
7

%I #31 Jun 25 2021 06:19:50

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

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

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

%N Decimal expansion of gamma - Ei(-1).

%C See crossrefs sequences for other comments, references, links, and formulas.

%H G. C. Greubel, <a href="/A239069/b239069.txt">Table of n, a(n) for n = 0..10000</a>

%H J. C. Lagarias, <a href="http://arxiv.org/abs/1303.1856">Euler's constant: Euler's work and modern developments</a>, arXiv:1303.1856 [math.NT], 2013-2014; Bull. Amer. Math. Soc., 50 (2013), 527-628; see p. 553.

%F Equals (the Euler-Mascheroni constant) - (the exponential integral at -1) = A001620 + A099285.

%F Equals (the Euler-Mascheroni constant) + (Gompertz's constant / e) = A001620 + (A073003 / A001113).

%F Equals Sum_{n>=1} (-1)^(n-1) / A001563(n) = Sum_{n>=1} (-1)^(n-1) / (n*n!).

%F Equals -Integral_{x=0..1} log(x)/exp(x) dx. - _Amiram Eldar_, Aug 01 2020

%F Equals (1/e) * Sum_{k>=1} H(k)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - _Amiram Eldar_, Jun 25 2021

%e 0.7965995992970531342836758655425240800732066293468...

%t RealDigits[EulerGamma - ExpIntegralEi[-1], 10, 100][[1]]

%o (PARI) Euler + eint1(1,1)[1] \\ _Michel Marcus_, Aug 01 2020

%Y Cf. A001008, A001113, A001563, A001620, A002805, A073003, A099285.

%K cons,nonn

%O 0,1

%A _Jonathan Sondow_, Mar 12 2014