A Padé approximant [L/M] is a rational function p(x)/q(x) with numerator degree L and denominator degree M, matching L+M+1 Taylor coefficients. Unlike Taylor series, Padé approximants can represent poles and continue functions beyond their radius of convergence. The [N/N] diagonal approximants often converge where Taylor series diverge.
Blue = exact | Red = Taylor | Green = Padé | Dashed = radius of convergence