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arXiv · 1708.01637

Matrix biorthogonal polynomials, associated polynomials and functions of the second kind

Amilcar Branquinho·Juan Carlos García-Ardila·Francisco Marcellán
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Abstract

In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A sort of Poincar\'{e}'s theorem for the ratio of two consecutive matrix functions solutions of a linear difference equation is also presented. Some new formulas connecting these families of matrix functions are given.

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Amilcar Branquinho, Juan Carlos García-Ardila, Francisco Marcellán. 2017-08-04. Matrix biorthogonal polynomials, associated polynomials and functions of the second kind. https://arxiv.org/abs/1708.01637

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