Ganzrationale Funktionen

Die allgemeine Form der ganzrationalen Funktion, auch Polynom genannt, sieht folgendermaßen aus:

f(x) = a0 + a1x1 + a2x2 + a3x3 + ... + anxn n ; a0 0

a0, a1, ... , an sind konstante Werte aus , wie z.B. 1, 3.2 oder ¾.
http://www.netalive.org/rationale-funktionen/chapters/2.html



Gebrochenrationale Funktionen

Sind g(x) und h(x) Polynome, also ganzrationale Funktionen, so nennt man die Funktion

f(x) = g(x) / h(x)

gebrochenrationale Funktion.
http://www.netalive.org/rationale-funktionen/chapters/3.html



In the case of one variable, x, a function is called a rational function if and only if it can be written in the form

f(x) = P(x)} /Q(x)

where P, and Q, are polynomial functions in x, and Q is not the zero polynomial.
http://en.wikipedia.org/wiki/Rational_function



A quotient of two polynomials P(z) and Q(z),
R(z)=(P(z))/(Q(z)),

is called a rational function, or sometimes a rational polynomial function. More generally, if P and Q are polynomials in multiple variables, their quotient is called a (multivariate) rational function. The term "rational polynomial" is sometimes used as a synonym for rational function. However, this usage is strongly discouraged since by analogy with complex polynomial and integer polynomial, rational polynomial should properly refer to a polynomial with rational coefficients.
http://mathworld.wolfram.com/RationalFunction.html

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Note added at 1 day2 hrs (2012-04-15 18:44:46 GMT)
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Integer Polynomial

A polynomial of the form
f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0

having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer arguments of x (Nagell 1951, p. 73). The set of integer polynomials is denoted Z[x]. Integer polynomials are sometimes also called "integral polynomials," although this usage should be deprecated due to its confusing use of the term "integral" as an adjective.

An integer polynomial is called primitive if the greatest common divisor (a_0,a_1,...,a_n)=1.
http://mathworld.wolfram.com/IntegerPolynomial.html

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Note added at 1 day2 hrs (2012-04-15 18:48:42 GMT)
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Rational Polynomial

A rational polynomial is a polynomial having rational coefficients.

While the term "rational polynomial" is sometimes used as a synonym for rational function, this usage is strongly discouraged since by analogy with complex polynomial and integer polynomial, "rational polynomial" should properly refer to a polynomial with rational coefficients.
http://mathworld.wolfram.com/RationalPolynomial.html

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Note added at 1 day2 hrs (2012-04-15 19:10:37 GMT)
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In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions.
http://en.wikipedia.org/wiki/Rational_function