rational function

Definitions

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).

Equivalents

Examples

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

“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.”

“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.”

CEFR level