A257819 Decimal expansion of the real part of li(-1).

7, 3, 6, 6, 7, 9, 1, 2, 0, 4, 6, 4, 2, 5, 4, 8, 5, 9, 9, 0, 1, 0, 0, 9, 6, 5, 2, 3, 0, 1, 4, 9, 6, 7, 1, 8, 6, 9, 8, 7, 7, 4, 6, 2, 3, 2, 8, 6, 1, 8, 0, 5, 0, 2, 6, 5, 9, 5, 5, 0, 3, 4, 0, 6, 9, 2, 3, 1, 7, 5, 8, 4, 3, 1, 4, 3, 0, 5, 7, 1, 3, 8, 3, 6, 5, 8, 4, 4, 2, 7, 8, 3, 2, 6, 0, 8, 8, 2, 4, 3, 3, 5, 9, 0, 6

Offset

-1,1

Comments

The logarithmic integral function li(z) has a cut along the negative real axis which causes therein a discontinuity in the imaginary part of li(z). The real part of li(z), however, is well behaved for any real z, except the singularity at z=+1. At z=-1, real(li(z)) attains its absolute maximum, and also its only local maximum, on the real interval (-infinity,+1). The corresponding imaginary part is described in A257820.

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 gamma+log(Pi)+Sum[k=1..infinity]((-1)^k*Pi^(2*k)/(2*k)!/(2*k)).

Example

0.073667912046425485990100965230149671869877462328618050265955...

Maple

evalf(Re(Li(-1)), 120); # Vaclav Kotesovec, May 11 2015

Mathematica

RealDigits[Re[LogIntegral[-1]], 10, 120][[1]] (* Vaclav Kotesovec, May 11 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(-1))

Crossrefs

Cf. A000796, A001620, A053510, A257817, A257818, A257820, A257821.

Sequence in context: A019819 A215693 A197028 * A182111 A344916 A023643

Adjacent sequences: A257816 A257817 A257818 * A257820 A257821 A257822

Keyword

nonn,cons

Author

Stanislav Sykora, May 11 2015

Status

approved