Generalised Airy polynomials

Abstract We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω ( x ; t , λ stretchy="false">) = exp − 1 3 + width="1em" ∈ R parameters λ > −1 and $t\in \mathbb{R}$?> . also investigate zeros recurrence coefficients polynomials. The sextic Freud \right)=\vert x{\vert }^{2\lambda +1}\enspace \mathrm{exp}\left(-{x}^{6}+t{x}^{2}\right),\quad stretchy="false">| 2 6 arises from a symmetrisation we study analogous this weight.