A283743 - OEIS

%I #23 Nov 28 2020 11:02:04

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

%C Can be considered the value of the divergent series -0! - 1! - 2! - ... ; see Lagarias reference Section 2.5. - _Harry Richman_, Jun 14 2020.

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Subfactorial.html">Subfactorial</a>

%F The real part of subfactorial(-1), that is the real part of Gamma(0,-1)/e.

%e 0.6971748832350660687654786819195515953171754309543695173200548...

%t RealDigits[ExpIntegralEi[1]/E, 10, 102][[1]]

%o (PARI) real(-eint1(-1)/exp(1)) \\ _Michel Marcus_, Jun 15 2020

%Y Cf. A000166 (subfactorials), A061382 (Pi/e, the imaginary part of subfactorial(-1)), A091725 (Ei(1)), A073003 (-exp(1)*Ei(-1)).

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Mar 15 2017