Generalised Airy Polynomials
arXiv:2012.13279 · doi:10.1088/1751-8121/abf019
Abstract
We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight \[ω(x;t,λ)=x^λ\exp\left(-\tfrac13x^3+tx\right),\qquad x\in \mathbb{R}^+,\] with parameters and . We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic Freud weight \[ω(x;t,λ)=|x|^{2λ+1}\exp\left(-x^6+tx^2\right), \qquad x\in \mathbb{R},\] arises from a symmetrisation of the generalised Airy weight and we study analogous properties of the polynomials orthogonal with respect to this weight.
22 pages, 1 figure. arXiv admin note: text overlap with arXiv:2004.00260. J. Phys. A: Math. Theor. (2021)