2020/12/31 by Peter A. Clarkson, Kerstin Jordaan · 1 citation
Mathematics · Physics and Astronomy · #math.CA #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8121/abf019
published as J. Phys. A: Math. Theor. 54 (2021) 185202 · 22 pages, 1 figure. arXiv admin note: text overlap with arXiv:2004.00260. J. Phys. A: Math. Theor. (2021)
arxiv created 2021/03/12 · arxiv updated 2021/04/21
We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω(x;t,λ)=xλexp(-\tfrac13x3+tx), x∈ ℝ+, with parameters λ>-1 and t∈ ℝ. We also investigate the zeros and recurrence coefficients of the polynomials. The generalised sextic Freud weight ω(x;t,λ)=|x|2λ+1exp(-x6+tx2), x∈ ℝ, arises from a symmetrisation of the generalised Airy weight and we study analogous properties of the polynomials orthogonal with respect to this weight.