A power series is an infinite series of the form $$ ext{f(x) = } \sum_{n=0}^{\infty} a_n (x - c)^n$$, where $$a_n$$ represents the coefficients, $$c$$ is the center of the series, and $$x$$ is the variable. Power series are used to represent functions as sums of their derivatives evaluated at a point, allowing for approximations and complex function analysis. They can converge within a certain radius from the center and are essential in understanding complex mappings and transformations.
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