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

%I A091723 #31 Feb 16 2025 08:32:52
%S A091723 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,
%T A091723 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,
%U A091723 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
%N A091723 Decimal expansion of the root x of Ei(x)=0, where Ei is the exponential integral.
%H A091723 Robert Price, <a href="/A091723/b091723.txt">Table of n, a(n) for n = 0..10000</a>
%H A091723 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.
%H A091723 Wikipedia, <a href="https://en.wikipedia.org/wiki/Exponential_integral">Exponential integral</a>.
%F A091723 Equals log(A070769). - _Amiram Eldar_, Aug 14 2020
%F A091723 Equals root x of li(exp(x)/x)=0 where li(x) is the logarithmic integral. - _Artur Jasinski_, Apr 19 2022
%e A091723 0.372507410781366634461991866580119133535689497771654...
%t A091723 RealDigits[ x /. FindRoot[ ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 102]][[1]] (* _Jean-François Alcover_, Oct 29 2012 *)
%t A091723 RealDigits[x /. FindRoot[LogIntegral[Exp[x]]/x, {x, 1/3}, WorkingPrecision -> 105]][[1]] (* _Artur Jasinski_, Apr 19 2022 *)
%o A091723 (PARI) solve(x=.3,1,real(eint1(-x))) \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A091723 Cf. A070769, A084945.
%K A091723 nonn,cons
%O A091723 0,1
%A A091723 _Eric W. Weisstein_, Feb 01 2004