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<p>In this paper, we study the iterated polynomial regularisation of the differential system related to the generalised Meixner orthogonal polynomials. We show how recurrence coefficients of these polynomials are related to the fifth Painlevé equation by using a sequence of resolutions of indeterminacy points of the initial differential system. We also examine how the final charts differential systems after the first iteration are related by Bäcklund transformations of the fifth Painlevé equation.</p>

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ON THE ITERATED POLYNOMIAL REGULARISATION OF THE DIFFERENTIAL SYSTEM RELATED TO THE GENERALISED MEIXNER ORTHOGONAL POLYNOMIALS

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月1日

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  • Galina Filipuk,
  • Hongmei Chen

摘要

In this paper, we study the iterated polynomial regularisation of the differential system related to the generalised Meixner orthogonal polynomials. We show how recurrence coefficients of these polynomials are related to the fifth Painlevé equation by using a sequence of resolutions of indeterminacy points of the initial differential system. We also examine how the final charts differential systems after the first iteration are related by Bäcklund transformations of the fifth Painlevé equation.