How to | Compute a Power Series
Calculus lets you approximate complicated functions with power series. The Wolfram Language lets you generate and work with power series for a huge range of functions.
Use Series to make a power series out of a function. The first argument is the function. The second argument has the form , where var is the variable, pt is the point around which to expand, and order is the order:
The "big-O" notation indicates that terms beyond are omitted:
Truncate the series to get a polynomial of degree 5 using Normal:
At , compare the polynomial and the original exponential function: