A364521 Decimal expansion of the solution to Ei(x) = x.

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

Offset: 0

Author

Michal Paulovic, Aug 15 2023

Keywords

• nonn
• cons

Comments

Fixed point of exponential integral.

Examples

			0.5276123472017420...
		

Links

• Eric Weisstein's World of Mathematics, Exponential Integral.
• Wikipedia, Exponential integral.

Crossrefs

Cf. A091723, A091725, A099285.

Programs

Maple

Digits:=101: fsolve(Ei(1,x)-x, x);

Mathematica

RealDigits[FindRoot[ExpIntegralE[1, x] - x, {x, 0.5}, WorkingPrecision -> 101][[1, 2]], 10, 101][[1]]

PARI

default(realprecision, 101); solve(x=0.5,0.6,eint1(x)-x)

PARI

solve(x=0.5,0.6,-Euler()-log(x)-suminf(k=1,(-x)^k/(k*k!))-x)