Rational Function

A quotient of two polynomials and ,

is called a rational function, or sometimes a rational polynomial function. More generally, if and are polynomials in multiple variables, their quotient is called a (multivariate) rational function. The term "rational polynomial" is sometimes used as a synonym for rational function. However, this usage is strongly discouraged since by analogy with complex polynomial and integer polynomial, rational polynomial should properly refer to a polynomial with rational coefficients.

A rational function has no singularities other than poles in the extended complex plane. Conversely, if a single-values function has no singularities other than poles in the extended complex plane, then it is a rational function (Knopp 1996, p. 137). In addition, a rational function can be decomposed into partial fractions (Knopp 1996, p. 139).

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