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A257818
Decimal expansion of the imaginary part of li(i), i being the imaginary unit.
4
2, 9, 4, 1, 5, 5, 8, 4, 9, 4, 9, 4, 9, 3, 8, 5, 0, 9, 9, 3, 0, 0, 9, 9, 9, 9, 8, 0, 0, 2, 1, 3, 2, 6, 7, 7, 2, 0, 8, 9, 4, 4, 6, 0, 3, 5, 2, 5, 1, 9, 2, 1, 5, 9, 0, 1, 2, 2, 7, 0, 4, 4, 3, 9, 2, 8, 3, 9, 4, 3, 5, 6, 4, 2, 1, 1, 0, 6, 0, 7, 2, 5, 0, 3, 4, 0, 8, 2, 6, 5, 3, 4, 8, 4, 9, 5, 9, 0, 9, 4, 9, 3, 4, 6, 7
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
Eric Weisstein's World of Mathematics, Logarithmic Integral
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
Sequence in context: A339799 A161934 A021038 * A195485 A336802 A011067
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, May 10 2015
STATUS
approved