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arXiv · 2012.13279

Generalised Airy Polynomials

Peter A. Clarkson·Kerstin Jordaan
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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.

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BibTeXRIS

Peter A. Clarkson, Kerstin Jordaan. 2020-12-24. Generalised Airy Polynomials. https://doi.org/10.1088/1751-8121%2Fabf019

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