论文标题
离散$ q $ -freud $ \ mathrm {ii} $正交多项式的渐近学来自$ q $ -riemann Hilbert问题
Asymptotics of Discrete $q$-Freud $\mathrm{II}$ orthogonal polynomials from the $q$-Riemann Hilbert Problem
论文作者
论文摘要
我们研究了一个Riemann-Hilbert问题（RHP），其解决方案对应于Ismail等人先前研究的一组$ Q $ - 正交多项式。使用RHP理论，我们根据多项式接近无穷大的程度来确定新的渐近造成结果。 RHP公式还使我们能够获得更多的属性。特别是，我们考虑了在$ q $ discrete晶格的翻译下，多项式及其渐近行为的类别如何变化，并确定相关$ q $-painlevé方程的渐近学。
We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the polynomials approach infinity. The RHP formulation also enables us to obtain further properties. In particular, we consider how the class of polynomials and their asymptotic behaviours change under translations of the $q$-discrete lattice and determine the asymptotics of related $q$-Painlevé equations.
