05/10/2008, 09:31 AM
I just made some pictures of real and imaginary part of \( \text{slog}_{sqrt{2}} \) below -2. The parts below -2 are just computed by taking logs of the part in -2..-1 which is computed by iterational regular iteration. But this coincides with directly computing the super exponential below -2 via the iterational regular iteration.
Here the real part:
Here the imaginary part:
Of course this is only one branch, of the many possible while whirling/analytically continuing around all the singularities at the negative integers.
As we have the symmetry \( \text{sexp}(\overline{z})=\overline{\text{sexp}(z)} \) except on the cut line, which is the real axis below -2, if we approach say -2.5 from below we get the negative imaginary value.
Here the real part:
Here the imaginary part:
Of course this is only one branch, of the many possible while whirling/analytically continuing around all the singularities at the negative integers.
As we have the symmetry \( \text{sexp}(\overline{z})=\overline{\text{sexp}(z)} \) except on the cut line, which is the real axis below -2, if we approach say -2.5 from below we get the negative imaginary value.