cp's OEIS Frontend

A239069 Decimal expansion of gamma - Ei(-1).

%I A239069 #34 Jan 03 2025 11:48:41
%S A239069 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 A239069 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 A239069 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 A239069 Decimal expansion of gamma - Ei(-1).
%C A239069 See crossrefs sequences for other comments, references, links, and formulas.
%D A239069 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 37, table 37:7:1 at page 355.
%H A239069 G. C. Greubel, <a href="/A239069/b239069.txt">Table of n, a(n) for n = 0..10000</a>
%H A239069 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 A239069 Equals (the Euler-Mascheroni constant) - (the exponential integral at -1) = A001620 + A099285.
%F A239069 Equals (the Euler-Mascheroni constant) + (Gompertz's constant / e) = A001620 + (A073003 / A001113).
%F A239069 Equals Sum_{n>=1} (-1)^(n-1) / A001563(n) = Sum_{n>=1} (-1)^(n-1) / (n*n!).
%F A239069 Equals -Integral_{x=0..1} log(x)/exp(x) dx. - _Amiram Eldar_, Aug 01 2020
%F A239069 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 A239069 0.7965995992970531342836758655425240800732066293468...
%t A239069 RealDigits[EulerGamma - ExpIntegralEi[-1], 10, 100][[1]]
%o A239069 (PARI) Euler + eint1(1,1)[1] \\ _Michel Marcus_, Aug 01 2020
%Y A239069 Cf. A001008, A001113, A001563, A001620, A002805, A073003, A099285.
%K A239069 cons,nonn
%O A239069 0,1
%A A239069 _Jonathan Sondow_, Mar 12 2014