# Taylor series

From Conservapedia

This article/section deals with mathematical concepts appropriate for late high school or early college. |

The **Taylor series** of a function is useful for approximating a mathematical function near to some particular point. For a function , the Taylor series about the point is

where each of the derivatives is to be evaluated at . If as the series converges, then it is exact. Otherwise, it can be used as an approximation. Often, Taylor series are performed around , in which case they are sometimes also known as a Maclaurin series.

### Examples of common Taylor series

#### Extensions of the Exponential Function

Consider the exponential of imaginary number ,

By the power laws then all complex numbers have an exponential,

.