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Branquinho, Amilcar and Foulquié Moreno, Ana and Fradi, Assil and Mañas Baena, Manuel
(2022)
*Riemann-Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painleve IV.*
Mathematics, 10
(8).
ISSN 2227-7390

PDF
Creative Commons Attribution. 392kB |

Official URL: http://dx.doi.org/10.3390/math10081205

## Abstract

In this paper, the Riemann-Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights-which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann-Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painleve IV equations are discussed.

Item Type: | Article |
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Additional Information: | © 2022 by the authors. |

Uncontrolled Keywords: | Multiple orthogonal polynomials; Recurrence coefficients; Differential equations; Asymptotics; models; Formulas; Respect |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 72291 |

Deposited On: | 06 Jun 2022 17:13 |

Last Modified: | 13 Jun 2022 08:30 |

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