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When is the composition of two power series even?

Part of: Series expansions

Published online by Cambridge University Press:  09 April 2009

Alan L. Horwitz  and
Lee A. Rubel
Alan L. Horwitz
Affiliation:
Pennsylvania State University, 25 Yearsley Mill Road Media, PA 19063, U.S.A.
Lee A. Rubel
Affiliation:
University of Illinois1409 West Green Street, Urbana, IL 61801, U.S.A
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Abstract

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If h is the composition of two formal power series f and g, and if h is even, what can be said about f and g? Some partial answers are given here.

MSC classification

Secondary: 30B10: Power series (including lacunary series)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 3 , June 1994 , pp. 415 - 420
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Baker, I. N. and Gross, Fred, ‘On factorizing entire functions’, Proc. London Math. Soc. 17 (1968), 69–76.Google Scholar
[2]Reznick, Bruce, ‘When is the iterate of a formal series odd?’, J. Austral. Math. Soc. (Series A) 28 (1979), 62–66.CrossRefGoogle Scholar
[3]Xin-Hou-Hua, , ‘Uniquely factorizable entire functions’, J. Math. Anal. Appl. 153 (1990), 11–17.CrossRefGoogle Scholar