Для системы, состоящей из функций {e λ 1 z , e λ 2 z }, изучаются асимптотические свойства её аппроксимаций Эрмита-Паде {π j n, m (z; e λ j ξ )} 2 j=1 . В частности, для любого z при n → ∞ найдена асимптотика поведения разностей e λ j z − π j n, m (z; e λ j ξ ), j = 1, 2. Полученные результаты дополняют аналогичные исследования Эрмита, Паде, Перрона, Д. Браесса, А. И. Аптекарева и других авторов.Ключевые слова: совершенная система функций, совместные аппроксимации Паде, аппроксимации Эрмита-Паде, асимптотические равенства, интегралы Эрмита. Hermitian Approximation of Two Exponents A. P. StarovoitovWe study the asymptotic properties of Hermite-Pade approximants {π j n, m (z; e λ j ξ )} 2 j=1 for a system consisting of functions {e λ 1 z , e λ 2 z }. In particular, we determine asymptotic behavior of differences e λ j z − π j n, m (z; e λ j ξ ) for j = 1, 2 and n → ∞ for any complex number z. The obtained results supplement research of Pade, Perron, D. Braess and A. I. Aptekarev dealing with study of the convergence of joinnt Pade approximants for systems of exponents.
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