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In this paper we regularize a second order differential system for the auxiliary functions related to the recurrence coefficients of the deformed Laguerre polynomials. We show how this system is related to the fifth Painlevé equation. We also discuss Hamiltonian structures of the initial and final charts differential systems. In addition, we present how Bäcklund transformations of the fifth Painlevé equation can be used to derive a discrete system for the auxiliary functions related to the recurrence coefficients.

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On the Regularisation of the Differential System Related to the Deformed Laguerre Polynomials

  • 会议论文

  • 发表日期：

    2025年

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  • Galina Filipuk

摘要

In this paper we regularize a second order differential system for the auxiliary functions related to the recurrence coefficients of the deformed Laguerre polynomials. We show how this system is related to the fifth Painlevé equation. We also discuss Hamiltonian structures of the initial and final charts differential systems. In addition, we present how Bäcklund transformations of the fifth Painlevé equation can be used to derive a discrete system for the auxiliary functions related to the recurrence coefficients.