Generalised Airy Polynomials

Abstract

We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω(x; t, λ)with parameters λ > −1 and t ∈ R. We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic Freud weightarises from a symmetrisation of the generalised Airy weight and we study analogous properties of the polynomials orthogonal with respect to this weight.