Analogs of Schmidt's Formula for Polyorthogonal Polynomials of the First Type

Given any system of Laurent-type power series, a criterion for the uniqueness of polyorthogonal polynomials of first type associated with this system is stated and proved, and explicit determinant representations generalizing E. Schmidt's formula for these polynomials are obtained. The proved statements supplement well-known results of the theory of orthogonal and polyorthogonal polynomials.