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Mathematics-Online course: Preparatory Course Mathematics - Analysis - Functions

Rational Function

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A rational function $ r$ with the degree of the nominator $ m$ and the degree of the denominator $ n$ 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 $ p$ and $ q$ 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.

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  automatically generated 1/9/2017