Pade approximants

Padé approximants are mathematical tools used to approximate complex functions with ratios of two simpler functions—specifically, ratios of polynomials. Unlike Taylor series, which may only work well near a specific point, Padé approximants can often provide accurate estimates over broader ranges by capturing a function’s behavior more effectively. They are especially useful in engineering and physics for modeling behaviors like oscillations or exponential growth, offering a compact way to approximate functions that are difficult to compute directly. Essentially, they find the best possible rational (fractional) approximation for a given function within a certain degree of accuracy.