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<p>An example of some iteration group in a ring of formal power series over a field of characteristic 0 is given in&#xa0;[<CitationRef CitationID="CR2">2</CitationRef>]. It is proved under the hypothesis that some system of combinatorial identities is valid. Here we discuss a proof that the mentioned system of identities is indeed satisfied. It is based on the Chu–Vandermonde identity. From this result we obtain an explicit formula for some one-parameter group of (truncated) formal power series. Moreover we describe some non-commutative groups of solutions of the third Aczél–Jabotinsky differential equation in the ring of truncated formal power series.</p>

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A combinatorial approach to prove an explicit form of some iteration groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月17日

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  • Harald Fripertinger,
  • Wojciech Jabłoński

摘要

An example of some iteration group in a ring of formal power series over a field of characteristic 0 is given in [2]. It is proved under the hypothesis that some system of combinatorial identities is valid. Here we discuss a proof that the mentioned system of identities is indeed satisfied. It is based on the Chu–Vandermonde identity. From this result we obtain an explicit formula for some one-parameter group of (truncated) formal power series. Moreover we describe some non-commutative groups of solutions of the third Aczél–Jabotinsky differential equation in the ring of truncated formal power series.