cp's OEIS Frontend

A257817 Decimal expansion of the real part of li(i), i being the imaginary unit.

%I A257817 #27 Feb 16 2025 08:33:25
%S A257817 4,7,2,0,0,0,6,5,1,4,3,9,5,6,8,6,5,0,7,7,7,6,0,6,1,0,7,6,1,4,1,2,7,8,
%T A257817 3,6,5,0,7,3,3,0,5,4,3,0,1,8,3,6,1,8,8,1,8,6,8,3,8,3,7,1,8,9,9,3,8,5,
%U A257817 8,0,3,7,7,6,9,5,3,1,3,0,8,5,0,9,3,3,7,9,7,0,7,6,0,4,9,2,9,2,1,2,0,0,1,5,3
%N A257817 Decimal expansion of the real part of li(i), i being the imaginary unit.
%C A257817 li(x) is the logarithmic integral function, extended to the whole complex plane. The corresponding imaginary part is in A257818.
%H A257817 Stanislav Sykora, <a href="/A257817/b257817.txt">Table of n, a(n) for n = 0..2000</a>
%H A257817 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>
%H A257817 Wikipedia, <a href="http://en.wikipedia.org/wiki/Logarithmic_integral_function">Logarithmic integral function</a>
%F A257817 Equals gamma + log(Pi/2) + Sum_{k>=1}((-1)^k*(Pi/2)^(2*k)/(2*k)!/(2*k)).
%F A257817 Equals Ci(Pi/2), the maximum value of the cosine integral along the real axis. - _Stanislav Sykora_, Nov 12 2016
%e A257817 0.47200065143956865077760610761412783650733054301836188186838371...
%p A257817 evalf(Re(Li(I)),120); # _Vaclav Kotesovec_, May 10 2015
%t A257817 RealDigits[Re[LogIntegral[I]], 10, 120][[1]] (* _Vaclav Kotesovec_, May 10 2015 *)
%o A257817 (PARI) li(z) = {my(c=z+0.0*I); \\ If z is real, convert it to complex
%o A257817   if(imag(c)<0, return(-Pi*I-eint1(-log(c))),
%o A257817   return(+Pi*I-eint1(-log(c)))); }
%o A257817   a=real(li(I))
%Y A257817 Cf. A001620, A019669, A094642, A257818.
%K A257817 nonn,cons
%O A257817 0,1
%A A257817 _Stanislav Sykora_, May 10 2015