# Taylor series

### From Glossary

For a function, having all derivatives, the series is:

where is the *k*-th derivative of Truncating the series at the *n*-th term, the error is given by:

This is a Taylor expansion, and for the Taylor series to equal the functional value, it is necessary that the error term approaches zero for each *n*:

In that case, there must exist in the line segment such that