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 J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 2, Pages 173–183 (Mi jsfu419)

Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions

Aleksandr J. Mkrtchyan

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: 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.

Keywords: Power series, analytic continuation, interpolating meromorphic function, indicator function.

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UDC: 517.55
Accepted: 25.04.2015
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Citation: Aleksandr J. Mkrtchyan, “Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 173–183

Citation in format AMSBIB
\Bibitem{Mkr15} \by Aleksandr~J.~Mkrtchyan \paper Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions \jour J. Sib. Fed. Univ. Math. Phys. \yr 2015 \vol 8 \issue 2 \pages 173--183 \mathnet{http://mi.mathnet.ru/jsfu419}