Am I suffering from knowledge blindness? The Taylor series article on Wikipedia doesn't seem to have a particularly impenetrable introduction. There's a couple

Am I suffering from knowledge blindness? The Taylor series article on Wikipedia doesn't seem to have a particularly impenetrable introduction. There's a couple phrases here and there that read a little bit awkwardly, but I think all the concepts here are covered in most high school mathematics curricula, except for the very end that briefly alludes to some introductory analysis concepts (the "analytic" portion). (Note that some of the concepts such as convergence here have links to additional articles) > In mathematics, the Taylor series of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named after Brook Taylor, who introduced them in 1715. > If zero is the point where the derivatives are considered, a Taylor series is also called a Maclaurin series, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. > The partial sum formed by the first n + 1 terms of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials. A function may differ from the sum of its Taylor series, even if its Taylor series is convergent. A function is analytic at a point x if it is equal to the sum of its Taylor series in some open interval (or open disk in the complex plane) containing x. This implies that the function is analytic at every point of the interval (or disk). https://en.wikipedia.org/wiki/Taylor_series https://en.wikipedia.org/wiki/Taylor_series