Mathematics-Online lexicon: Rational Functions

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	Mathematics-Online lexicon:
	Rational Functions

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A rational function

with the degree of the nominator

and the degree of the denominator

is the quotient of two polynomials:

$\displaystyle r(x) = \frac{p(x)}{q(x)} = \frac{a_0+a_1x+\cdots+a_mx^m}{b_0+b_1x+\cdots+b_nx^n} \,.$

This representation is irreducible if

and

have no common linear factor.

Then the zeros of the denominator are called poles. The order of the pole corresponds to the multiplicity of the zero.

Examples:

automatically generated 4/ 8/2008