power series

Noun

Meaning

the sum of terms containing successively higher integral powers of a variable

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Examples

An important point is that the p-adic field, or respectively the real or complex field, corresponding to a prime ideal, plays exactly the role, in arithmetic, that the field of power series in the neighborhood of a point plays in the theory of functions: that is why one calls it a local field. André Weil

A formal power series ring consists of formal power series : together with multiplication and addition that mimic those for convergent series. Source: Internet

Any polynomial can be easily expressed as a power series around any center c, although most of the coefficients will be zero since a power series has infinitely many terms by definition. Source: Internet

Alternatively, one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series to construct the Taylor series of a function, by virtue of Taylor series being power series. Source: Internet

As a holomorphic function, the Laplace transform has a power series representation. Source: Internet

But the general construction of a completion of a metric space is more involved than what is needed here, and would make formal power series seem more complicated than they are. Source: Internet

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