# Generalised Airy polynomials

Clarkson, Peter A., Jordaan, Kerstin (2021) Generalised Airy polynomials. Journal of Physics A: Mathematical and Theoretical, . ISSN 1751-8113. E-ISSN 1751-8121. (doi:10.1088/1751-8121/abf019) (KAR id:87261)

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## Abstract

We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight $\omega(x;t,\lambda)=x^{\lambda}\exp\left(-\tfrac13x^3+tx\right),\qquad x\in \mathbb{R}^+$ with parameters $\lambda>-1$ and $t\in \mathbb{R}$. We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic Freud weight $\omega(x;t,\lambda)=|x|^{2\lambda+1}\exp\left(-x^6+tx^2\right), \qquad x\in \mathbb{R}$ arises from a symmetrisation of the generalised Airy weight and we study analogous properties of the polynomials orthogonal with respect to this weight.

Item Type: Article 10.1088/1751-8121/abf019 Semi-classical orthogonal polynomials, generalised Airy weight; generalised sextic Freud weight; moments; recurrence coefficients; zeros; asymptotics Q Science Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Peter Clarkson 22 Mar 2021 15:38 UTC 30 Jan 2022 23:11 UTC https://kar.kent.ac.uk/id/eprint/87261 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-8777-5284
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