A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it in terms of the solution of a system of partial differential equations.

In the case of two orthogonality measures the differential equations become ordinary. For Angelesco systems, the result is illustrated numerically.

中文翻译：

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Nevai类的多个正交多项式的递归系数极限的微分方程

研究了来自Nevai类的多个正交多项式的最近邻递归系数的极限性质。即，假设最近邻系数沿晶格射线具有极限，我们用偏微分方程组的解来描述它。

在两个正交度量的情况下，微分方程变得很普通。对于Angelesco系统，将以数字方式说明结果。