On the explicit representation of polyorthogonal polynomials

New concepts are introduced in the work: an admissible index, an almost perfect system of functions. Using these concepts for an arbitrary system of power series of Laurent type is formulated and proved a criterion for the uniqueness of a associated with this system of a poly orthogonal polynomial. The explicit form of this polynomial is found, as well as the explicit form of polynomials standing in the numerator and denominator of the corresponding of Padé approximations. The propositions proved complement the well-known results the in theory of polyorthogonal polynomials and Padé approximations.