login
A257817
Decimal expansion of the real part of li(i), i being the imaginary unit.
4
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, 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, 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
OFFSET
0,1
COMMENTS
li(x) is the logarithmic integral function, extended to the whole complex plane. The corresponding imaginary part is in A257818.
LINKS
Eric Weisstein's World of Mathematics, Logarithmic Integral
FORMULA
Equals gamma + log(Pi/2) + Sum_{k>=1}((-1)^k*(Pi/2)^(2*k)/(2*k)!/(2*k)).
Equals Ci(Pi/2), the maximum value of the cosine integral along the real axis. - Stanislav Sykora, Nov 12 2016
EXAMPLE
0.47200065143956865077760610761412783650733054301836188186838371...
MAPLE
evalf(Re(Li(I)), 120); # Vaclav Kotesovec, May 10 2015
MATHEMATICA
RealDigits[Re[LogIntegral[I]], 10, 120][[1]] (* Vaclav Kotesovec, May 10 2015 *)
PROG
(PARI) li(z) = {my(c=z+0.0*I); \\ If z is real, convert it to complex
if(imag(c)<0, return(-Pi*I-eint1(-log(c))),
return(+Pi*I-eint1(-log(c)))); }
a=real(li(I))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, May 10 2015
STATUS
approved