

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
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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*Ieint1(log(c))),
return(+Pi*Ieint1(log(c)))); }
a=imag(li(I))


CROSSREFS

Cf. A019669, A257817.
Sequence in context: A299792 A161934 A021038 * A195485 A011067 A135008
Adjacent sequences: A257815 A257816 A257817 * A257819 A257820 A257821


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, May 10 2015


STATUS

approved



