论文标题
广义通风多项式
Generalised Airy Polynomials
论文作者
论文摘要
我们考虑半古典正交多项式相对于广义的通风\ [ω（x; t; t; t，λ）= x^λ\ exp \ left（ - \ tfrac13x^3+tx \ tx \ right） \ mathbb {r} $。我们还研究了多项式的零和复发系数。广义的六五弗罗伊德重量\ [ω（x; t，λ）= | x |^{2λ+1} \ exp \ left（-x^6+tx^2 \ right），\ qquad x \ in \ in \ mathbb {r}，r}，\ r}，\ r}，\ r}，\ r}，\ r}，\ r}，\ r}，\ r}，\ r}，\ r}，我们研究的一般体重和我们的拟合性属性或我们的象征性属性，或者我们的拟合性属性属性。这个重量。
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.
