Characteristics of the sum of a multidimensional series - Makarov, V. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We study the relationship between the asymptotic behavior of coefficients of a multidimensional series of exponents and the asymptotic behavior of its sum near a point on the boundary of the domain of convergence. Growth characteristics, an order ρ_Q(a), and a type σ_Q β(a) in an octant Q(a) are determined. The dependence of growth characteristics on the coordinates of points of the boundary of the domain of convergence is established.