 Rational function

A rational function is a quotient $p/q$ of polynomials, with $q$ nonzero. After cancelling common factors, it defines a holomorphic map from the Riemann sphere to itself.

A rational function is a type of mathematical function that can be expressed as the ratio of two polynomial functions. Specifically, a rational function can be written in the form: \[ R(x) = \frac{P(x)}{Q(x)} \] where \( P(x) \) and \( Q(x) \) are polynomials, and \( Q(x) \) is not equal to zero.