Tetration for complex bases

Authors

William Paulsen, Arkansas State University - JonesboroFollow

Document Type

Article

Publication Title

Advances in Computational Mathematics

Abstract

In this paper we will consider the tetration, defined by the equation F(z + 1) = bF(z) in the complex plane with F(0) = 1, for the case where b is complex. A previous paper determined conditions for a unique solution the case where b is real and b > e1/e. In this paper we extend these results to find conditions which determine a unique solution for complex bases. We also develop iteration methods for numerically approximating the function F(z), both for bases inside and outside the Shell-Thron region.

First Page

243

Last Page

267

DOI

10.1007/s10444-018-9615-7

Publication Date

2-2-2019

Recommended Citation

Paulsen, William, "Tetration for complex bases" (2019). Faculty Publications. 8.
https://arch.astate.edu/scm-mathfac/8