A369883 - OEIS

%I #14 Aug 05 2024 13:40:17

%S 3,6,1,3,2,8,6,1,6,8,8,8,2,2,2,5,8,4,6,9,7,1,6,1,6,5,7,6,7,8,7,3,9,9,

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

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

%N Decimal expansion of Integral_{x=0..1} x/(1 - log(x)) dx.

%H Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 397.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Exponential_integral">Exponential Integral</a>.

%F Equals Integral_{x=0..1} x/(1 - log(x)) dx.

%F Equals - e^2*Ei(-2), where Ei(x) is the Exponential Integral function [Shamos].

%F Equals Integral_{x=0..oo} dx/(e^x*(x + 2)) [Shamos].

%e 0.361328616888222584697161657678739938954590641...

%t RealDigits[-E^2 * ExpIntegralEi[-2], 10, 120][[1]] (* _Amiram Eldar_, Feb 04 2024 *)

%o (PARI) intnum(x=0,1,x/(1-log(x)))

%Y Cf. A073003, A091725, A099285.

%K nonn,cons

%O 0,1

%A _Claude H. R. Dequatre_, Feb 04 2024