arXiv
Open Access
2020
Generalised Airy Polynomials
Peter A. Clarkson
Kerstin Jordaan
Abstrak
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 $λ>-1$ and $t\in \mathbb{R}$. 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.
Penulis (2)
P
Peter A. Clarkson
K
Kerstin Jordaan
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2020
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓