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Taylor series

The Taylor series for polynomes is



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



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

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