Advances in Computational Mathematics

, Volume 45, Issue 1, pp 243–267 | Cite as

Tetration for complex bases

  • William PaulsenEmail author


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.


Tetration Abel’s functional equation Iteration 

Mathematics Subject Classification (2010)

26A18 30D05 39B12 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Arkansas State UniversityJonesboroUSA

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