Analytic continuation of multiple power series by means of coefficients interpolation

One way to explore on analytic function is to expand it to a power series. The coefficients of a power series expansion contain the information of its analytic continuation. One possible approach to treat analytic continuation problem is to interpolate the coefficients by values of an entire or a meromorphic functions. We consider the problem of continuability into a sectorial domain for multiple power series centered at the origin. The conditions of the mentioned continuability is given in terms of function interpolating the coefficients of power series.