A276763 Decimal expansion of the imaginary part of a fixed point of the logarithmic integral li(z) in C.

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

Offset

1,1

Comments

See A276762 for the real part, as well as detailed comments and links.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Example

2.06592220237066218898810461125410843001424985319006732838579118...

Mathematica

RealDigits[Im[z/.FindRoot[LogIntegral[z] == z, {z, 2+I}, WorkingPrecision -> 100]]][[1]] (* Vaclav Kotesovec, Oct 30 2016 *)

Prog

(PARI) \\ z may be t_INT, t_REAL, or t_COMPLEX except 0 or 1
li(z)=
{
  my(sgn=(-1)^if(real(z)<1, imag(z)<0, imag(z)<=0));
  sgn*Pi*I - eint1(-log(z));
}
default(realprecision, 2100); \\ Execution:
Eps_= 4.0*10.0^(-default(realprecision));
z=1+I; zlast=0; \\ Initialize and iterate
for(k=1, 1e6, z=li(z); if(abs(z-zlast)<Eps_, break); zlast=z);
imag(z) \\ Display the result

Crossrefs

Cf. A276762 (real part), A070769.

Sequence in context: A111520 A326040 A145419 * A338465 A142354 A105110

Adjacent sequences: A276760 A276761 A276762 * A276764 A276765 A276766

Keyword

nonn,cons

Author

Stanislav Sykora, Oct 28 2016

Status

approved