# rational function

## English

### Noun

rational function (plural rational functions)

1. () Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator).
• 1960, J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd Edition, American Mathematical Society, page 184,
Our first problem is that of interpolation in prescribed points to a given function by a rational function whose poles are given.
• 1970, Ellis Horowitz, Algorithms for Symbolic Integration of Rational Functions, University of Wisconsin–Madison, page 24,
By Theorem 2.3.2., we have that the right-hand side of this equation can be equal to a rational function only if that rational function is equal to zero.
• 2000, Alan F. Beardon, Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer, page 45,
Let ${\mathcal {C}}$ be the class of continuous maps of $\mathbb {C} _{\infty }$ into itself and let ${\mathcal {R}}$ be the subclass of rational functions. [] Now ${\mathcal {R}}$ is a closed subset of ${\mathcal {C}}_{\infty }$ because if the rational functions $R_{n}$ converge uniformly to $R$ on the complex sphere, then $R$ is analytic on the sphere and so it too is rational.