Formal power series with coefficients tending to 0
In algebra, the ring of restricted power series is the subring of a formal power series ring that consists of power series whose coefficients approach zero as degree goes to infinity.[1] Over a non-archimedean complete field, the ring is also called a Tate algebra. Quotient rings of the ring are used in the study of a formal algebraic space as well as rigid analysis, the latter over non-archimedean complete fields.
Over a discrete topological ring, the ring of restricted power series coincides with a polynomial ring; thus, in this sense, the notion of "restricted power series" is a generalization of a polynomial.
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_{k=0}^{n}{\binom {n}{k}}x^{k}} holds for x = 0 only if 00 = 1. Similarly, rings of powerseries require x0 to be defined as 1 for all specializations of x. For example...
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