# Tetration for complex bases

@article{Paulsen2019TetrationFC, title={Tetration for complex bases}, author={William H. Paulsen}, journal={Advances in Computational Mathematics}, year={2019}, volume={45}, pages={243-267} }

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…

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