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 -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.
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