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

Renato Álvarez-Nodarse; Antonio J. Durán

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

Classical Analysis and ODEs 2013-09-16 v1

Authors: Renato Álvarez-Nodarse , Antonio J. Durán

Abstract

Let $(p_n)_n$ be either the $q$ -Meixner or the $q$ -Laguerre polynomials. We form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of two consecutive $p_n$ : $q_n=p_n+\beta_np_{n-1}$ , $\beta_n\in \RR$ . Using the concept of $\D$ -operator, we generate sequences $(\beta_n)_n$ for which the polynomials $(q_n)_n$ are orthogonal with respect to a measure and common eigenfunctions of a higher order $q$ -difference operator.

Keywords

orthogonal polynomials q-series and q-analogues pseudodifferential operators

Cite

@article{arxiv.1309.3296,
  title  = {Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations},
  author = {Renato Álvarez-Nodarse and Antonio J. Durán},
  journal= {arXiv preprint arXiv:1309.3296},
  year   = {2013}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:1302.0881, arXiv:1307.1326

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

Abstract

Keywords

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