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<p>We demonstrate that discrete <i>m</i>-functions with eventually periodic continued fraction coefficients have an algebraic relationship to their second solution if and only if the periodic part of the sequence of continued fraction coefficients is doubly palindromic. In this setting, doubly palindromic means that each sequence is a repeated concatenation of two palindromes and a compatibility condition between the lengths of these palindromes is satisfied.</p>

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Discrete m-functions with doubly palindromic continued fraction coefficients

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Hunter Handley,
  • Brian Simanek

摘要

We demonstrate that discrete m-functions with eventually periodic continued fraction coefficients have an algebraic relationship to their second solution if and only if the periodic part of the sequence of continued fraction coefficients is doubly palindromic. In this setting, doubly palindromic means that each sequence is a repeated concatenation of two palindromes and a compatibility condition between the lengths of these palindromes is satisfied.