Iterating exponential functions with cyclic exponents-Reference-Cited by-同舟云学术

Iterating exponential functions with cyclic exponents

Published:1989-03 Issue:2 Volume:105 Page:357-375
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Baker I. N.,Rippon P. J.

Abstract

This paper is concerned with expressions of the form

where fa(x) = ax. Thus we have

Such expressions have been described variously as continued exponentials, iterated exponentials, towers of exponents or hyperpowers. We shall frequently make use of their elementary properties, as for example

and

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. A note on infinite exponentials;Baker;Fibonacci Quart,1985

2. [2] Baker I. N. and Rippon P. J. . Towers of exponents and other composite maps. (To appear in the Edrei-Fuchs Special Issue of Complex Variables Theory Appl.)

3. Convergence of infinite exponentials with complex elements

4. De formulis exponentialibus replicatus;Euler;Acta Academiae Petropolitanae,1777

5. Stable Orbits and Bifurcation of Maps of the Interval

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Infinite random power towers;Electronic Journal of Probability;2024-01-01

2. Computer research of the holomorphic dynamics of exponential and linear-exponential maps;Computer Research and Modeling;2018-08

3. Iterated cyclic exponentials and power functions with extra-periodic first coefficients;Sbornik: Mathematics;2010-02-28

4. Generalized Iteration;Computational Methods and Function Theory;2004-03

5. Summation of power series by continued exponentials;Journal of Mathematical Physics;1996-08