A257818 Decimal expansion of the imaginary part of li(i), i being the imaginary unit.

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

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

Cf. A019669, A257817.

Sequence in context: A339799 A161934 A021038 * A195485 A336802 A011067

Adjacent sequences: A257815 A257816 A257817 * A257819 A257820 A257821

Keyword

nonn,cons

Author

Stanislav Sykora, May 10 2015

Status

approved