Adv Comput Math https://doi.org/10.1007/s10444-018-9615-7 William Paulsen Received: 9 January 2018 / Accepted: 22 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper we will consider the tetration, defined by the equation F(z + F(z) 1) = b 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 1/e real and b> 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. Keywords Tetration · Abel’s functional equation · Iteration Mathematics Subject Classification (2010) 26A18 · 30D05 · 39B12 1 Background Much research has already been done on the tetration function, whose name comes from tetra- (four) and iteration. Addition by a positive integer n can be thought of as repeated incrementing, multiplication by n is done by repeated addition, and Communicated by: Aihui Zhou William Paulsen firstname.lastname@example.org Arkansas State University, Jonesboro, AR, USA W. Paulsen exponentiation by n is repeated multiplication. So a
Advances in Computational Mathematics – Springer Journals
Published: Jun 2, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud