Unique positive solutions to -discrete equations associated with orthogonal polynomials
arXiv:2011.06270 · doi:10.1080/10236198.2021.1944121
Abstract
Boelen et al. (2010) deduced a -discrete Painlevé 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.
Final version will be published in Journal of Difference Equations and Applications, 13 pages, 0 figures