A091723 Decimal expansion of the root x of Ei(x)=0, where Ei is the exponential integral.

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

Offset: 0

Author

Eric W. Weisstein, Feb 01 2004

Keywords

• nonn
• cons

Examples

			0.372507410781366634461991866580119133535689497771654...
		

Links

• Robert Price, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Exponential Integral.
• Wikipedia, Exponential integral.

Crossrefs

Cf. A070769, A084945.

Programs

Mathematica

RealDigits[ x /. FindRoot[ ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 102]][[1]] (* Jean-François Alcover, Oct 29 2012 *)
RealDigits[x /. FindRoot[LogIntegral[Exp[x]]/x, {x, 1/3}, WorkingPrecision -> 105]][[1]] (* Artur Jasinski, Apr 19 2022 *)

PARI

solve(x=.3,1,real(eint1(-x))) \\ Charles R Greathouse IV, Apr 14 2014

Formula

Equals log(A070769). - Amiram Eldar, Aug 14 2020

Equals root x of li(exp(x)/x)=0 where li(x) is the logarithmic integral. - Artur Jasinski, Apr 19 2022