About analytical continuation of the multiple power series with the m-homogeneous polynomial matrix method to the generalized star Mittag-Leffler

The work is devoted to the analytical continuation of the multiple power series in the class of areas generalizing stars. With the help of multiple power series reanalysis by m-homogeneous polynomials constructed continuation of this series of in (m 1,..., m n ) -circular area, which are a natural generalization of circular areas in C n. Based on this decomposition, the multiple of a power series analytically continues maximum m-star region called m-star Mittag-Leffler function f defined by this row. This analytic continuation is a superposition of m-homogeneous polynomials, which decomposes a power series with an infinite triangular matrix, which elements do not depend on the function f. The paper contains an example, when m-star Mittag-Leffler differs from a normal star Mittag-Leffler.