Taylor & Maclaurin Series

The function to expand into a Taylor polynomial. It must be smooth (differentiable) at the expansion point, like exp(x) or sin(x).

The variable of the series. The polynomial is written in powers of (variable − x₀).

The point the series is centred on. The polynomial is most accurate near x₀ and drifts away from the function further out. With x₀ = 0 the result is called a Maclaurin series.

The highest power kept in the polynomial. A higher order tracks the function more closely over a wider range, but has more terms.