|
%I #13 Sep 29 2016 02:38:27
%S 2,6,8,4,5,1,0,3,5,0,8,2,0,7,0,7,6,5,2,5,0,2,3,8,2,6,4,0,4,8,7,2,3,8,
%T 6,8,5,3,1,0,1,7,9,7,3,4,5,9,8,5,5,1,6,3,5,2,2,0,4,1,4,8,6,4,5,0,2,6,
%U 4,1,1,3,3,6,3,1,7,6,7,2,4,4,8,9,3,6,2,5,0,2,2,0,1,2,5,4,8,5,2,1,5,3,6,5,0
%N Decimal expansion of the derivative of logarithmic integral at its positive real root.
%C Since the real root location of li(x) is the Soldner's constant A070769, this constant equals 1/log(A070769). It is also the inverse of the unique real root A091723 of the exponential integral function Ei(x).
%H Stanislav Sykora, <a href="/A276709/b276709.txt">Table of n, a(n) for n = 1..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Logarithmic_integral_function">Logarithmic integral function</a>
%F Equals 1/log(A070769) and 1/A091723.
%e 2.68451035082070765250238264048723868531017973459855163522041486450...
%t 1/x/.FindRoot[ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 104] (* _Vaclav Kotesovec_, Sep 27 2016 *)
%o (PARI) li(z) = {my(c=z+0.0*I); \\ Computes li(z) for any complex z
%o if(imag(c)<0,return(-Pi*I-eint1(-log(c))),return(+Pi*I-eint1(-log(c))));}
%o a = 1/log(solve(x=1.1,2.0,real(li(x)))) \\ Computes this constant
%Y Cf. A070769, A091723, A257821.
%K nonn,cons
%O 1,1
%A _Stanislav Sykora_, Sep 15 2016
|
