rational function

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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 be the class of continuous maps of into itself and let be the subclass of rational functions. [] Now is a closed subset of because if the rational functions converge uniformly to on the complex sphere, then is analytic on the sphere and so it too is rational.