Tetration for complex bases

  title={Tetration for complex bases},
  author={William H. Paulsen},
  journal={Advances in Computational Mathematics},
  • William H. Paulsen
  • Published 1 February 2019
  • Mathematics
  • Advances in Computational Mathematics
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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