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arXiv · 2011.06270

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

Tomas Lasic Latimer
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Abstract

Boelen et al. (2010) deduced a $q$-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.

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Tomas Lasic Latimer. 2020-11-12. Unique positive solutions to $q$-discrete equations associated with orthogonal polynomials. https://doi.org/10.1080/10236198.2021.1944121

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