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arXiv · 2403.18669

Orthogonal Polynomials with a Singularly Perturbed Airy Weight

Chao Min·Yuan Cheng
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Abstract

We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.

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Chao Min, Yuan Cheng. 2024-03-27. Orthogonal Polynomials with a Singularly Perturbed Airy Weight. https://arxiv.org/abs/2403.18669

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