cp's OEIS Frontend

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

%I A364521 #11 Feb 16 2025 08:34:06
%S A364521 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,
%T A364521 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,
%U A364521 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
%N A364521 Decimal expansion of the solution to Ei(x) = x.
%C A364521 Fixed point of exponential integral.
%H A364521 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.
%H A364521 Wikipedia, <a href="https://en.wikipedia.org/wiki/Exponential_integral">Exponential integral</a>.
%e A364521 0.5276123472017420...
%p A364521 Digits:=101: fsolve(Ei(1,x)-x, x);
%t A364521 RealDigits[FindRoot[ExpIntegralE[1, x] - x, {x, 0.5}, WorkingPrecision -> 101][[1, 2]], 10, 101][[1]]
%o A364521 (PARI) default(realprecision, 101); solve(x=0.5,0.6,eint1(x)-x)
%o A364521 (PARI) solve(x=0.5,0.6,-Euler()-log(x)-suminf(k=1,(-x)^k/(k*k!))-x)
%Y A364521 Cf. A091723, A091725, A099285.
%K A364521 nonn,cons
%O A364521 0,1
%A A364521 _Michal Paulovic_, Aug 15 2023