Power series

Infinite sum of monomials

In mathematics, a power series (in one variable) is an infinite series of the form ∑ n = 0 ∞ a n ( x − c) n = a 0 + a 1 ( x − c) + a 2 ( x − c) 2 + … {\displaystyle \sum _{n=0}^{\infty }a_{n}\left(x-c\right)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\dots } where a n {\displaystyle a_{n}} represents the coefficient of the nth term and c is a constant called the center of the series. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function.

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