rational function

rational function (plural rational functions)

1. (mathematics, complex analysis, algebraic geometry) 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 ${\displaystyle {\mathcal {C}}}$ be the class of continuous maps of ${\displaystyle \mathbb {C} _{\infty }}$ into itself and let ${\displaystyle {\mathcal {R}}}$ be the subclass of rational functions. […] Now ${\displaystyle {\mathcal {R}}}$ is a closed subset of ${\displaystyle {\mathcal {C}}_{\infty }}$ because if the rational functions ${\displaystyle R_{n}}$ converge uniformly to ${\displaystyle R}$ on the complex sphere, then ${\displaystyle R}$ is analytic on the sphere and so it too is rational.

• function, meromorphic function

• proper rational function

• rational function on Wikipedia.Wikipedia