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arXiv · 2204.11528

Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions

Alan D. Sokal
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Abstract

I analyze an unexpected connection between multiple orthogonal polynomials, $d$-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.

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Alan D. Sokal. 2022-04-25. Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions. https://doi.org/10.1090/btran%2F133

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