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Wiktionary The Free Dictionary

rational function

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English

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Noun

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

Hypernyms

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Hyponyms

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Translations

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function expressible as the quotient of polynomials

References

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