A276763 - OEIS

%I #10 Nov 04 2016 03:08:13

%S 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,

%T 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,

%U 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

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

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

%H Stanislav Sykora, <a href="/A276763/b276763.txt">Table of n, a(n) for n = 1..2000</a>

%e 2.06592220237066218898810461125410843001424985319006732838579118...

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

%o (PARI) \\ z may be t_INT, t_REAL, or t_COMPLEX except 0 or 1

%o li(z)=

%o {

%o   my(sgn=(-1)^if(real(z)<1,imag(z)<0,imag(z)<=0));

%o   sgn*Pi*I - eint1(-log(z));

%o }

%o default(realprecision,2100); \\ Execution:

%o Eps_= 4.0*10.0^(-default(realprecision));

%o z=1+I;zlast=0; \\ Initialize and iterate

%o for(k=1,1e6,z=li(z);if(abs(z-zlast)<Eps_,break);zlast=z);

%o imag(z) \\ Display the result

%Y Cf. A276762 (real part), A070769.

%K nonn,cons

%O 1,1

%A _Stanislav Sykora_, Oct 28 2016