Combinatorial orthogonal expansions

1994/06/29 by Anne de Médicis, de Médicis, Anne, Dennis W. Stanton +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #math.CA #math.CO

paper · pdf · doi:10.48550/arxiv.math/9406226

arxiv created 1994/06/29 · arxiv updated 2009/11/30

Abstract

The linearization coefficients for a set of orthogonal polynomials are given explicitly as a weighted sum of combinatorial objects. Positivity theorems of Askey and Szwarc are corollaries of these expansions.

Related

• Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials
• Sur une generalisation des coefficients binomiaux
• Combinatorics of orthogonal polynomials of type R_I
• Alternative Orthogonal Polynomials
• Orthogonal polynomials of several variables