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5 - Combinatorics of Orthogonal Polynomials and their Moments

Published online by Cambridge University Press:  07 October 2020

By
Jiang Zeng
Edited by
Howard S. Cohl  and
Mourad E. H. Ismail
Howard S. Cohl
Affiliation:
National Institute of Standards and Technology
Mourad E. H. Ismail
Affiliation:
University of Central Florida
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Summary

The aim of this chapter is to introduce the formal theory of general orthogonal polynomials and present the two dual combinatorial approaches due to Foata for the special function aspects of the orthogonal polynomials, and to Flajolet and Viennot for the lattice paths models used for the moments and general orthogonal polynomials. After reviewing the standard interplay between orthogonal polynomials and combinatorics, influenced by their pioneering works, we will report on some recent topics developed in this cross-cutting field of these two branches of mathematics.

Keywords

combinatoricsorthogonal polynomialsSheffer orthogonal polynomialslinearization coefficientsmomentsq-polynomialsMacMahon master theoremcombinatorics of continued fractions
Type
Chapter
Information
Lectures on Orthogonal Polynomials and Special Functions , pp. 280 - 334
Publisher: Cambridge University Press
Print publication year: 2020

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