English

Unique positive solutions to $q$-discrete equations associated with orthogonal polynomials

Classical Analysis and ODEs 2021-10-18 v2

Abstract

Boelen et al. (2010) deduced a qq-discrete Painlev\'e equation satisfied by the recurrence coefficients of orthogonal polynomials and conjectured that the equation had a unique positive solution. We prove their conjecture and discuss related work in the area, highlighting a potentially unifying methodology.

Keywords

Cite

@article{arxiv.2011.06270,
  title  = {Unique positive solutions to $q$-discrete equations associated with orthogonal polynomials},
  author = {Tomas Lasic Latimer},
  journal= {arXiv preprint arXiv:2011.06270},
  year   = {2021}
}

Comments

Final version will be published in Journal of Difference Equations and Applications, 13 pages, 0 figures

R2 v1 2026-06-23T20:07:29.198Z