rational function

plural rational functions

1. algebraic geometryAny 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).

   Our first problem is that of interpolation in prescribed points to a given function by a rational function whose poles are given.

   1960, J. L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd edition, American Mathematical Society, page 184

   2 more examples

   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.

   1970, Ellis Horowitz, Algorithms for Symbolic Integration of Rational Functions, University of Wisconsin-Madison, page 24

   Let #92;mathcal#123;C#125; be the class of continuous maps of #92;mathbb#123;C#125;#95;#92;infty into itself and let #92;mathcal#123;R#125; be the subclass of rational functions.[…]Now #92;mathcal#123;R#125; is a closed subset of #92;mathcal#123;C#125;#95;#92;infty because if the rational functions R#95;n converge uniformly to R on the complex sphere, then R is analytic on the sphere and so it too is rational.

   2000, Alan F. Beardon, Iteration of Rational Functions: Complex Analytic Dynamical Systems, Springer, page 45