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<p>In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of multiple variables. The aim of the second part is to remove ambiguities connected with the Right Distributive Law for formal power series of one variable as well as to provide analogues of that law in the multivariable case.</p>

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On composition and Right Distributive Law for formal power series of multiple variables

  • 期刊论文

  • 发表日期：

    2025年1月23日

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  • Dariusz Bugajewski,
  • Alessia Galimberti,
  • Piotr Maćkowiak

摘要

In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of multiple variables. The aim of the second part is to remove ambiguities connected with the Right Distributive Law for formal power series of one variable as well as to provide analogues of that law in the multivariable case.