A criterion for the existence and uniqueness of polyorthogonal polynomials of the first type

A criterion for the uniqueness of polyorthogonal polynomials of type I associated with an arbitrary system of power series of the Laurent type is formulated and proved. An explicit form of these polynomials and an explicit form for the corresponding polynomial of the second kind is found. The proven statements complement well-known results in the theory of orthogonal and polyorthogonal polynomials.