A099285 Decimal expansion of -Ei(-1), negated exponential integral at -1.

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

Offset

0,1

Comments

The divergent series g(x=1,m) = 1^m*1! - 2^m*2! + 3^m*3! - 4^m*4! + ..., m=>-1, is closely related to the value of -Ei(-1). We discovered that g(x=1,m) = (-1)^m*(A040027(m) - A000110(m+1)*Ei(1,1)*exp(1)), see A163940. We observe that Ei(1,1) = E(1,1,1) = -Ei(-1) is the constant given above and that Ei(1,1)*exp(1) = A073003 is Gompertz's constant. - Johannes W. Meijer, Oct 16 2009

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Exponential Integral

Formula

-Ei(-n) = Integral_{a=n..Infinity} ( Integral_{b=1..Infinity} 1/e^(a*b) db ) da , n>0 (According to Mathematica). - Mats Granvik, May 25 2013

Equals the difference between the absolute values of A239069 and A001620. - R. J. Mathar, Mar 07 2016

From Amiram Eldar, Aug 01 2020: (Start)

Equals Integral_{x=1..oo} log(x)/exp(x) dx.

Equals Integral_{x=0..oo} exp(-exp(x)) dx.

Equals Integral_{x=0..oo} x*exp(x-exp(x)) dx. (End)

Example

0.219383934395520273677163775460121649031047293406908207577978613...

Maple

Digits:=105: evalf(-Ei(-1)); evalf(Ei(1, 1)); # Johannes W. Meijer, Oct 16 2009

Mathematica

RealDigits[ ExpIntegralE[1, 1], 10, 105][[1]]

Prog

(PARI) eint1(1, 1) \\ Michel Marcus, Aug 01 2020

Crossrefs

Cf. A073003.

Sequence in context: A160510 A298738 A124776 * A249264 A188108 A166890

Adjacent sequences: A099282 A099283 A099284 * A099286 A099287 A099288

Keyword

cons,nonn

Author

Robert G. Wilson v, Oct 08 2004

Extensions

Definition corrected by Johannes W. Meijer, Jul 26 2009

Corrected Name (minus 1, not 1), Stanislav Sykora, May 18 2012

Status

approved