First, assume that the function f(x) does, in fact, have a power series representation about x = a, A function may not be equal to its Taylor series, although its Taylor series converges at every point. The Taylor series of a function is the limit of that function’s Taylor polynomials with the increase in degree if the limit exists. The polynomial formed by taking some initial terms of the Taylor series is popular as Taylor polynomial. Taylor’s theorem is providing quantitative estimates on the error. In this topic, we will see the concept of Taylor series and Taylor Series Formula with examples.Ī function can be approximated by using a finite number of terms in its Taylor series. For the expansion of mathematical series, it is used extensively. But, it was formally introduced by the English mathematician Brook Taylor in 1715. This concept was formulated by the Scottish mathematician James Gregory. These terms are calculated from the values of the function’s derivatives at a single point. The Taylor series formula is the representation of any function as an infinite sum of terms.
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