Taylor’s Theorem
What are Taylor Series?
Taylor series is the expansion of any real or complex valued function. It is used to define the value of a function when the value of its derivatives at a particular point is defined.
It is widely used in Computer Science, Calculus, and other branches of science.
What is Taylor Series Formula?
The Taylor series formula for the expansion of a function f(x) is,
f(x) = f(a) + f′(a)(x − a) + f′′(a)/2! × (x − a)2+ f′′′(a)/3! × (x − a)3+ f(4)(a)/4! × (x − a)4+ … + f(n)(a)/n! × (x − a)n
Who Invented Taylor Series Formula?
Scottish mathematician James Gregory was the first to give an idea about the Taylor series and it was finally perfected by English mathematician Brook Taylor in 1715.
Who Invented Taylor Series Formula?
Scottish mathematician James Gregory was the first to explain the concept of the Taylor series and it was later fully developed by English mathematician Brook Taylor in the year 1715.
What is difference between Taylor Series and Maclaurin Series?
Taylor series is a series which is used to represent the value of a function with respect to the infinite sum of the derivative of the polynomial or other function with respect to a fixed point.
While the Maclaurian series is a special case of the Taylor series and it is the expansion of the function with respect to zero as the single point.
Taylor Series
Taylor Series is the series which is used to find the value of a function. It is the series of polynomials or any function and it contains the sum of infinite terms. Each successive term in the Taylor series expansion has a larger exponent or a higher degree term than the preceding term. We take the sum of the initial four, and five terms to find the approximate value of the function but we can always take more terms to get the precise value of the function.
In this article, we will learn about the Taylor Series expansion, formula, Maclaurin Series, and others in this article.
Table of Content
- Taylor Series Expansion
- Taylor Series & Maclaurin Series
- Taylor’s Series Formula
- Taylor Series Theorem Proof
- Taylor Series of Sin x
- Taylor Series of Cos x
- Taylor Series in Several Variables
- Maclaurin Series
- Applications of Taylor Series