2012/07/14 by Jang Soo Kim, Kim, Jang Soo, Dennis Stanton +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #math.CA #math.CO
paper · pdf · doi:10.48550/arxiv.1207.3446
23 pages
arxiv created 2013/02/08 · arxiv updated 2013/02/11
New formulas for the nth moment of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.