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%I #14 Oct 06 2020 12:13:53
%S 4,3,7,5,1,8,5,1,5,3,0,6,1,8,9,8,3,8,5,4,7,0,9,0,6,5,6,4,8,5,2,5,8,4,
%T 2,9,1,6,2,3,8,2,3,1,1,4,6,7,7,0,1,1,8,6,4,9,6,1,0,4,4,4,9,1,8,0,3,7,
%U 2,1,5,6,3,0,8,9,3,4,7,2,8,1,7,5,9,8,8,1,8,2,3,9,9,0,9,5,9,5,1,4,1,7,9,7,8
%N Decimal expansion of the imaginary part of the fixed point of -exp(z) in C congruent with the branch K=1 of log(z)+2*Pi*K*i.
%C Imaginary part of the complex constant z_2 whose real part is in A276759 (see the latter entry for more information).
%H Stanislav Sykora, <a href="/A276760/b276760.txt">Table of n, a(n) for n = 1..2000</a>
%H Stanislav Sykora, <a href="https://doi.org/10.3247/SL6Math16.002">Fixed points of the mappings exp(z) and -exp(z) in C</a>, 2016.
%F Let z_2 = A276759+i*A276760. Then z_2 = -exp(z_2) = log(-z_2)+2*Pi*i = -W_-1(1).
%e 4.375185153061898385470906564852584291623823114677011864961044...
%t RealDigits[Im[-ProductLog[-1, 1]], 10, 105][[1]] (* _Jean-François Alcover_, Nov 12 2016 *)
%o (PARI) default(realprecision,2050);eps=5.0*10^(default(realprecision))
%o M(z,K)=log(-z)+2*Pi*K*I; \\ the convergent mapping (any K)
%o K=1;z=1+I;zlast=z;
%o while(1,z=M(z,K);if(abs(z-zlast)<eps,break);zlast=z);
%o imag(z)
%Y Fixed points of -exp(z): z_0: A030178, and z_2: A276759 (real part), A276761 (modulus).
%Y Fixed points of +exp(z): z_1: A059526, A059527, A238274, and z_3: A277681, A277682, A277683.
%K nonn,cons
%O 1,1
%A _Stanislav Sykora_, Nov 12 2016
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