A257817 Decimal expansion of the real part of li(i), i being the imaginary unit.

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

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Eric Weisstein's World of Mathematics, Logarithmic Integral

Wikipedia, Logarithmic integral function

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

Cf. A001620, A019669, A094642, A257818.

Sequence in context: A078220 A256040 A363746 * A246710 A139346 A133390

Adjacent sequences: A257814 A257815 A257816 * A257818 A257819 A257820

Keyword

nonn,cons

Author

Stanislav Sykora, May 10 2015

Status

approved