About integrated representation like Mellina-Barnsa of the solution of system of the polynomial equations of the special kind

Mellin-Barnes integrals represent hyper geometrical functions - the most extensive class of special functions. These integrals are applied to calculation of groups of a monodromy of A-hyper geometrical systems of the differential equations. Besides, Mellin-Barnes integrals found a broad application in theoretical physics, in particular, in problems of quantum electrodynamics. Separately it is necessary to emphasize a role of integrals of Mellin-Barnes in the theory of the algebraic equations. The research problem of convergence of Mellin-Barnes integrals in boundary points of their areas of convergence is of interest. For integral of Mellin-Barnes submitting solutions of the algebraic equations this task it was considered earlier. Integrated Mellin transform for the decision of the general polynomial system of the algebraic equations was investigated in a number of modern works in which direct transformation was calculated by means of linearization of system (replacement of a variable of a special look). For system of the polynomial equations of a special look the theorem in which an integrated impression like Mellin-Barnes of monomial function a solution vector of system with the indication of a set of convergence is gained is proved. The proof consists of two parts. Function representation of a solution vector in the integral like Mellin-Barnes locates in the first part. In the second part of the proof the set of convergence of the received integral, namely boundary points of area of convergence is investigated. It is proved that any boundary point won’t belong to convergence area, the integral submitting the decision of polynomial system of a special look meets in sectorial area.