Power series
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.