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Taylor series

The Taylor series for polynomes is

 


Explanation

Take the polynome Pn(x) of degree n. The development in powers of x − a has the form

Multiple differentiation of Pn(x) gives



For x = a you get





Calculation of a0a1a2, ... , an and substitution in Pn shows

 


Example 1

The exponential function has for every value of x the series development

 


History

The English mathematician Brook Taylor (1685 - 1731) is best known for the Taylor series.


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