7. Analytic Continuation of Power Series by Means of Interpolating the Coefficients by Meromorphic Functions
Aleksandr J. Mkrtchyan · Journal of Siberian Federal University Mathematics & Physics · 2015
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.