Taylor series

The Taylor series is a formula that determines a polynomial approximation in x of some mathematical function f(x) centred at some value x0:

     

 

where f(m) represents the mth derivative with respect to x of the function f.

In the special case where x0 = 0, the series is known as the Maclaurin series of f(x):

 

     

The Taylor and Maclaurin series expansions are used elsewhere in this help file to provide polynomial approximations to probability distribution functions.

Read on: The Central Limit Theorem

 

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