Taylor series
From Conservapedia
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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,
.
