power series

== English == === Alternative forms === power-series (attributive use) === Noun === power series (plural power series) (mathematics, mathematical analysis) Any infinite series of the general form ∑ i = 0 ∞ a i ( x − c ) i {\displaystyle \sum _{i=0}^{\infty }a_{i}(x-c)^{i}} . 1899, Oskar Bolza, The Theory of Functions, 2013, Reprint, Books on Demand, page 69, From this theorem (for which in many cases Cauchy's theorem on double sums may be substituted) follow easily the rules for the multiplication and division of power series, Taylor's theorem for power series along with the rules for differentiation of power series and series of power series. ==== Usage notes ==== The constant c is sometimes called the centre of the power series, and is often 0. ==== Hyponyms ==== Maclaurin series, Taylor series Laurent series ==== Derived terms ==== formal power series ==== Related terms ==== radius of convergence interval of convergence ==== Translations ==== === References === Oregon State University Mathematics Dept Web study guide - Introduction to Power Series Power Series, Folkmar Bornemann, Eric W. Weisstein, MathWorld