Taylor series expansion

Definition

A Taylor series expansion is a way to represent a function as an infinite sum of terms that are calculated from the values of its derivatives at a single point. It provides an approximation of the function near that point.

Related terms

Convergence:

The process by which a Taylor series approaches the value of the original function as more terms are included in the sum.

Radius of convergence: The distance from the center point where a Taylor series expansion can be used to approximate the function accurately.

Maclaurin series: A special case of the Taylor series expansion, where the center point is chosen as x=0.