Analytic Continuation of Power Series by Means of Interpolating the Coefficients by Meromorphic Functions
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https://elib.sfu-kras.ru/handle/2311/16804Author:
Mkrtchyan, Aleksandr J.
Мкртчян, Александр Д.
Date:
2015-05Abstract:
We study the problem of analytic continuation of a power series across an open arc on the boundary of
the circle of convergence. The answer is given in terms of a meromorphic function of a special form
that interpolates the coefficients of the series. We find the conditions for the sum of the series to extend
analytically to a neigbourhood of the arc, to a sector defined by the arc, or to the whole complex plane
except some arc on the convergence disk В работе исследуется вопросы об аналитическом продолжении степенного ряда через открытую
дугу на границе круга сходимости. Ответ на такой вопрос дан в терминах мероморфной функции
специального вида, интерполирующей коэффициенты ряда. Получены условия при которых сумма
ряда аналитически продолжается в некоторую окрестность дуги в сектор, определенный дугой,
во всю комплексную плоскость, кроме некоторой дуги
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