Using D-operators to construct orthogonal polynomials satisfying higher\n order q-difference equations

2013/09/12 by R. Álvarez-Nodarse, Antonio J. Durán, Álvarez-Nodarse, Renato +1
Mathematics · Physics and Astronomy · #33D45 #33E30 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1309.3296

openalex publication_date 2013/09/12 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

Let (p_n)_n be either the q-Meixner or the q-Laguerre polynomials. We\nform a new sequence of polynomials (q_n)_n by considering a linear\ncombination of two consecutive p_n: q_n=p_n+\β_np_n-1, \β_n\∈\n RR. Using the concept of D-operator, we generate sequences (\β_n)_n\nfor which the polynomials (q_n)_n are orthogonal with respect to a measure\nand common eigenfunctions of a higher order q-difference operator.\n

Citations

• The Stieltjes moments problem for rapidly decreasing functions

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