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Composition of Involutive Power Series, and Reversible Series

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Abstract

For each natural number n, we characterise the invertible series (under composition) that are the composition of n proper involutions. We work with formal power series in one variable over a field of characteristic zero. We also describe the reversible series (those conjugate to their own inverses), and the series that are the composition of n reversible series.

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Authors and Affiliations

  1. Mathematics Department, National University of Ireland, Co. Kildare, Ireland

    Anthony G. O’Farrell

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  1. Anthony G. O’Farrell
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Correspondence to Anthony G. O’Farrell.

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Dedicated to Walter Hayman on his eightieth birthday

Supported by SFI grant RFP05 MAT0003.

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O’Farrell, A.G. Composition of Involutive Power Series, and Reversible Series. Comput. Methods Funct. Theory 8, 173–193 (2008). https://doi.org/10.1007/BF03321681

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  • DOI: https://doi.org/10.1007/BF03321681

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