cp's OEIS Frontend

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

%I A276763 #10 Nov 04 2016 03:08:13
%S A276763 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 A276763 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 A276763 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 A276763 Decimal expansion of the imaginary part of a fixed point of the logarithmic integral li(z) in C.
%C A276763 See A276762 for the real part, as well as detailed comments and links.
%H A276763 Stanislav Sykora, <a href="/A276763/b276763.txt">Table of n, a(n) for n = 1..2000</a>
%e A276763 2.06592220237066218898810461125410843001424985319006732838579118...
%t A276763 RealDigits[Im[z/.FindRoot[LogIntegral[z] == z, {z, 2+I}, WorkingPrecision -> 100]]][[1]] (* _Vaclav Kotesovec_, Oct 30 2016 *)
%o A276763 (PARI) \\ z may be t_INT, t_REAL, or t_COMPLEX except 0 or 1
%o A276763 li(z)=
%o A276763 {
%o A276763   my(sgn=(-1)^if(real(z)<1,imag(z)<0,imag(z)<=0));
%o A276763   sgn*Pi*I - eint1(-log(z));
%o A276763 }
%o A276763 default(realprecision,2100); \\ Execution:
%o A276763 Eps_= 4.0*10.0^(-default(realprecision));
%o A276763 z=1+I;zlast=0; \\ Initialize and iterate
%o A276763 for(k=1,1e6,z=li(z);if(abs(z-zlast)<Eps_,break);zlast=z);
%o A276763 imag(z) \\ Display the result
%Y A276763 Cf. A276762 (real part), A070769.
%K A276763 nonn,cons
%O A276763 1,1
%A A276763 _Stanislav Sykora_, Oct 28 2016