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Published online by Cambridge University Press: 07 October 2020
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.
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