On Analytic Continuation of the Power Series Outsideof the Convergence Disc

Author(s)

On Analytic Continuation of the Power Series Outsideof the Convergence Disc Levon Nurbekyan

In current work we discuss the issue of the analytic continuation of a power series alonga logarithmic spiral outside of the convergence disc. A necessary and sufficient condition interms of the interpolating entire function is obtained. Moreover, the relation in between thepossibility of analytic continuation and the density of the lacunas of a power series is studied.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/82 Armenian Journal of Mathematics, 4(1) 25-43

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Keywords

power series, analytic continuation, interpolating entire function, lacunas, den-sity.

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