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Decimal expansion of the root x of Ei(x)=0, where Ei is the exponential integral.
5

%I #30 Jun 07 2022 11:12:53

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

%H Robert Price, <a href="/A091723/b091723.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%F Equals log(A070769). - _Amiram Eldar_, Aug 14 2020

%F Equals root x of li(exp(x)/x)=0 where li(x) is the logarithmic integral. - _Artur Jasinski_, Apr 19 2022

%e 0.372507410781366634461991866580119133535689497771654...

%t RealDigits[ x /. FindRoot[ ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 102]][[1]] (* _Jean-François Alcover_, Oct 29 2012 *)

%t RealDigits[x /. FindRoot[LogIntegral[Exp[x]]/x, {x, 1/3}, WorkingPrecision -> 105]][[1]] (* _Artur Jasinski_, Apr 19 2022 *)

%o (PARI) solve(x=.3,1,real(eint1(-x))) \\ _Charles R Greathouse IV_, Apr 14 2014

%Y Cf. A070769, A084945.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Feb 01 2004