The Combinatorics of Al-Salam-Chihara q-Laguerre polynomials

2008/10/17 by Anisse Kasraoui, Kasraoui, Anisse, Dennis Stanton +3
Mathematics · #05A30. #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Primary 05A18 #Secondary 05A15 #math.CA #math.CO #msc:05A15 #msc:05A18 #msc:05A30.

paper · pdf · doi:10.48550/arxiv.0810.3232

23 pages, to appear in Adv. in Appl. Math.

openalex publication_date 2008/10/17 · arxiv created 2010/04/30 · arxiv updated 2010/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe various aspects of the Al-Salam-Chihara q-Laguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients. It is remarkable that the corresponding moment sequence appears also in the recent work of Postnikov and Williams on enumeration of totally positive Grassmann cells.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Related

• Combinatorics of (q,y)-Laguerre polynomials and their moments
• The combinatorics of q-Charlier polynomials
• Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
• Specializations of generalized Laguerre polynomials
• Probabilistic aspects of Al-Salam-Chihara polynomials