08/12/2009, 08:59 PM
Actually I am somewhat confused about the continuation of
\( f_n = \log_a^{[n]}\circ \exp_b^{[n]} \)
for some \( n \) from the real axis to the complex plane (via the method described by Jay some posts ago, i.e. considering a/the path \( \gamma \) from a point on the real axis to \( z \), looking at its image under \( \exp_b^{[n]} \) and determine the value of the subsequently following logarithms by their continuation along the image of that path).
Has anyone a clear view to which points \( f_n \) can be continued, is it even entire?
\( f_n = \log_a^{[n]}\circ \exp_b^{[n]} \)
for some \( n \) from the real axis to the complex plane (via the method described by Jay some posts ago, i.e. considering a/the path \( \gamma \) from a point on the real axis to \( z \), looking at its image under \( \exp_b^{[n]} \) and determine the value of the subsequently following logarithms by their continuation along the image of that path).
Has anyone a clear view to which points \( f_n \) can be continued, is it even entire?