ABSTRACT

We study the logarithmic asymptotic of multiple orthogonal polynomials arising in a mixed-type Hermite–Padé approximation problem associated with the rational perturbation of a Nikishin system of functions. The formulas obtained allow to give exact estimates of the rate of convergence of the corresponding Hermite–Padé approximants.

中文翻译：

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多级 Hermite-Padé 多项式的对数渐近

摘要

我们研究了在与 Nikishin 函数系统的有理扰动相关的混合型 Hermite-Padé 近似问题中出现的多个正交多项式的对数渐近性。获得的公式可以准确估计相应的 Hermite-Padé 近似值的收敛速度。