cp's OEIS Frontend

A276709 Decimal expansion of the derivative of logarithmic integral at its positive real root.

%I A276709 #14 Feb 16 2025 08:33:36
%S A276709 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 A276709 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 A276709 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 A276709 Decimal expansion of the derivative of logarithmic integral at its positive real root.
%C A276709 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 A276709 Stanislav Sykora, <a href="/A276709/b276709.txt">Table of n, a(n) for n = 1..2000</a>
%H A276709 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>
%H A276709 Wikipedia, <a href="https://en.wikipedia.org/wiki/Logarithmic_integral_function">Logarithmic integral function</a>
%F A276709 Equals 1/log(A070769) and 1/A091723.
%e A276709 2.68451035082070765250238264048723868531017973459855163522041486450...
%t A276709 1/x/.FindRoot[ExpIntegralEi[x] == 0, {x, 1}, WorkingPrecision -> 104] (* _Vaclav Kotesovec_, Sep 27 2016 *)
%o A276709 (PARI) li(z) = {my(c=z+0.0*I); \\ Computes li(z) for any complex z
%o A276709 if(imag(c)<0,return(-Pi*I-eint1(-log(c))),return(+Pi*I-eint1(-log(c))));}
%o A276709 a = 1/log(solve(x=1.1,2.0,real(li(x)))) \\ Computes this constant
%Y A276709 Cf. A070769, A091723, A257821.
%K A276709 nonn,cons
%O A276709 1,1
%A A276709 _Stanislav Sykora_, Sep 15 2016