Taylor series

SymPy expressions can be expanded as Taylor series using the series() function from the SymPy module.

Taylor series about $x=a$ is given by:

$$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}a}{n!}(x-a)^n$$

where $f^{(n)}$ is the $n^{th}$ derivative of $f$.

For a generic expansion, we only need to specify the expression and the variable in the expansion for which the expression is to be expanded.

series(f(x), x)

or

f(x).series(x)

Let’s see a basic implementation of the series() function below: