Dictionary

rational function en · NOUN

Meanings

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).
   • 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:
   • 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:

Forms

Hypernyms

function · meromorphic function

Hyponyms

proper rational function

Translations (6)

hu racionális függvény (function expressible as the quotient of polynomials) · tr rasyonel fonksiyon (function expressible as the quotient of polynomials) · pl funkcja wymierna (function expressible as the quotient of polynomials) · ru рациона́льная фу́нкция (function expressible as the quotient of polynomials) · de rationale Funktion (function expressible as the quotient of polynomials) · fi rationaalifunktio (function expressible as the quotient of polynomials)