: Mathematics: power series

mathematical analysis > complex analysis > power series

mathematical analysis > calculus > series > power series

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power series

In mathematics, a power series (in one variable) is an infinite series of the form
${\\displaystyle \\sum _{n=0}^{\\infty }a_{n}\\left(x-c\ ight)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\\dots }$
where a_n represents the coefficient of the nth term and c is a constant. 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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Power_series)

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