Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions
Classical Analysis and ODEs
2024-07-09 v2 Combinatorics
Abstract
I analyze an unexpected connection between multiple orthogonal polynomials, -orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot's combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal.
Keywords
Cite
@article{arxiv.2204.11528,
title = {Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions},
author = {Alan D. Sokal},
journal= {arXiv preprint arXiv:2204.11528},
year = {2024}
}
Comments
41 pages, LaTeX2e. Version 2 corrects a few small typos, uses the term "coefficient matrix" instead of "representing matrix" for a sequence of monic polynomials, and adds two references. To be published in the Transactions of the AMS