Tetration for complex bases

Autor: William Paulsen
Rok vydání: 2018
Předmět:
Zdroj: Advances in Computational Mathematics. 45:243-267
ISSN: 1572-9044
1019-7168
DOI: 10.1007/s10444-018-9615-7
Popis: 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.
Databáze: OpenAIRE
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