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Even and odd entire functions

Part of: Series expansions Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

A. F. Beardon
A. F. Beardon
Affiliation:
Centre for Mathematical Sciences University of CambridgeWilberforce Road Cambridge CB3 0WBEngland e-mail: afb@dpmms.cam.ac.uk
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Abstract

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We examine what can be said about a polynomial p and an entire function f given that p o f is an even, or an odd, function.

Keywords

entire functionseven functionsuniformization

MSC classification

Secondary: 30B10: Power series (including lacunary series) 30D05: Functional equations in the complex domain, iteration and composition of analytic functions 30D20: Entire functions, general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 19 - 24
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Horwitz, A. L., ‘Even compositions of entire functions and related matters’, J. Austral. Math. Soc. (Ser. A) 63 (1997), 225–237.CrossRefGoogle Scholar
[2]Horwitz, A. L. and Rubel, L. A., ‘When is the composition of two power series even?’, J. Austral. Math. Soc. (Ser. A) 56 (1994), 415–420.CrossRefGoogle Scholar