

A099285


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


8



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
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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, MathWorld: 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


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]]


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



