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Power series

A power series in one variable is an infinite sum of the form

where the (complex) number an is the coefficient of the n-th term.



If the series converges only in an environment of the point c one will often write the power series (with other coefficients) in the form

For that reason, occasionally the power series is called as being centered around c.


Example 1

You can write the function f (x) = x2 + 2x + 3 as a power series around c = 0 as

and around c = 1 as


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