A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is
In this report we construct a family of holomorphic functions β_λ,μ (s) which behave asymptotically like iterated exponentials as |s| →∞ in the right half plane. Each β_λ,μ satisfies a convenient functional relationship with nested exponentials; and has a series expansion that converges in a half-plane. They provide a nearness to the dynamics of the map e^μ z : ℂ→ℂ and behave asymptotically as a fractional iteration would behave. These objects are used to describe the various orbits of thearXiv:2208.05328v1 fatcat:5gb4smhekbddjgbozbycz7gz5m