论文标题
差异方程的差异方程式的正交多项式的复发系数具有奇异的laguerre型重量
Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight
论文作者
论文摘要
我们关注的是一元正交多项式相对于奇异的laguerre型重量。通过使用梯子运算符方法，我们得出了一个复杂的二阶差异方程式的复杂系统。这使我们能够得出复发系数的大$ N $渐近扩展。此外，我们还获得了复发系数的差分方程的系统。
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations satisfied by the recurrence coefficients. This allows us to derive the large $n$ asymptotic expansions of the recurrence coefficients. In addition, we also obtain a system of differential-difference equations for the recurrence coefficients.
