OFFSET
1,1
COMMENTS
li(x) is the logarithmic integral function, extended to the whole complex plane. The corresponding real part is in A257817.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Logarithmic Integral
Wikipedia, Logarithmic integral function
FORMULA
Equals (Pi/2)*(1+Sum_{k>=0}((-1)^k*(Pi/2)^(2*k)/(2*k+1)!/(2*k+1))).
EXAMPLE
2.941558494949385099300999980021326772089446035251921590122704439...
MAPLE
evalf(Im(Li(I)), 120); # Vaclav Kotesovec, May 10 2015
evalf(Pi/2*(1+Sum(((-1)^k*(Pi/2)^(2*k)/(2*k+1)!/(2*k+1)), k=0..infinity)), 120); # Vaclav Kotesovec, May 10 2015
MATHEMATICA
RealDigits[Im[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=imag(li(I))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, May 10 2015
STATUS
approved