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

中文翻译：

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关于多项式多项式的显式表示

在工作中，引入了新的概念：可接受的索引，几乎完美的功能系统。将这些概念用于Laurent型幂级数的任意系统，可以制定和证明与该系统相关的多正交多项式的唯一性准则。找到该多项式的显式形式，以及对应的Padé逼近的分子和分母中的多项式的显式形式。证明的断言补充了多正交多项式和Padé逼近理论中的著名结果。