# Solving F(z + 1) = bF(z) in the complex plane

```@article{Paulsen2017SolvingF,
title={Solving F(z + 1) = bF(z) in the complex plane},
author={William H. Paulsen and Samuel Cowgill},
year={2017},
volume={43},
pages={1261-1282}
}```
• Published 7 March 2017
• Mathematics
The generalized tetration, defined by the equation F(z+1) = bF(z) in the complex plane with F(0) = 1, is considered for any b > e1/e. By comparing other solutions to Kneser’s solution, natural conditions are found which force Kneser’s solution to be the unique solution to the equation. This answers a conjecture posed by Trappmann and Kouznetsov. Also, a new iteration method is developed which numerically approximates the function F(z) with an error of less than 10−50 for most bases b, using…
3 Citations
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