On the existence and uniqueness of type i Hermite–Padé polynomials

New concepts are introduced in the work. They are quite normal index and a quite perfect system of functions. Using these concepts, a uniqueness criterion was formulated and proved, explicit determinant representations of type I Hermite–Padé polynomials for an arbitrary system of power series were obtained. The results obtained complement and generalize the well-known result in the theory of Hermite–Padé approximations.