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### Power series

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

where the (complex) number *a*_{n} is the coefficient of the *n*-th term.

##### Explanation

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*) = *x*^{2} + 2*x* + 3 as a power series around *c = *0 as

and around *c = *1 as