A Maclaurin series is a power series
which provides an approximation for y near x=0.
It is a way of “coding” functions into a standard form, i.e. power series.
It doesn’t work for all functions, but it does work for a lot of them.
The coefficient can be calculated from
For many functions the approximation can be made as good as you like, or even as good as you like for x as big as you like, by calculating enough terms of the power series.
Maclaurin series can be used
- to find approximate solutions to differential equations which can’t be solved otherwise
- to calculate values of functions like for different values of x
- to make it easier to differentiate functions
- to make it possible to integrate functions which can’t be integrated otherwise.