cp's OEIS Frontend

A283743 Decimal expansion of Ei(1)/e, where Ei is the exponential integral function.

%I A283743 #28 Feb 16 2025 08:33:43
%S A283743 6,9,7,1,7,4,8,8,3,2,3,5,0,6,6,0,6,8,7,6,5,4,7,8,6,8,1,9,1,9,5,5,1,5,
%T A283743 9,5,3,1,7,1,7,5,4,3,0,9,5,4,3,6,9,5,1,7,3,2,0,0,5,4,8,0,7,7,8,9,4,5,
%U A283743 4,1,1,5,1,9,5,1,4,4,2,6,9,6,2,9,1,0,0,5,3,0,3,0,3,3,3,9,1,1,4,0,0,6
%N A283743 Decimal expansion of Ei(1)/e, where Ei is the exponential integral function.
%C A283743 Can be considered the value of the divergent series -0! - 1! - 2! - ... ; see Lagarias reference Section 2.5. - _Harry Richman_, Jun 14 2020.
%D A283743 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 44, equation 44:5:10 at page 426.
%H A283743 Jeffrey 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; Bull. Amer. Math. Soc., 50 (2013), 527-628.
%H A283743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.
%H A283743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Subfactorial.html">Subfactorial</a>.
%F A283743 Equals Re(subfactorial(-1)) = Re(Gamma(0,-1)/e).
%F A283743 Equals Sum_{k=1..oo} (-1)^k*psi(k)/Gamma(k), where psi denotes the digamma function (see Spanier and Oldham). - _Stefano Spezia_, Jan 04 2025
%e A283743 0.6971748832350660687654786819195515953171754309543695173200548...
%t A283743 RealDigits[ExpIntegralEi[1]/E, 10, 102][[1]]
%o A283743 (PARI) real(-eint1(-1)/exp(1)) \\ _Michel Marcus_, Jun 15 2020
%Y A283743 Cf. A000166 (subfactorials), A061382 (Pi/e, the imaginary part of subfactorial(-1)), A091725 (Ei(1)), A073003 (-exp(1)*Ei(-1)).
%K A283743 nonn,cons
%O A283743 0,1
%A A283743 _Jean-François Alcover_, Mar 15 2017