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By using [[polynomial long division]] and the partial fraction technique from algebra, any rational function can be written as a sum of terms of the form ''1 / (az + b)<sup>k</sup>'' + ''p(z)'', where ''a'' and ''b'' are complex, ''k'' is an integer, and ''p(z)'' is a polynomial . Just as [[polynomial factorization]] can be generalized to the [[Weierstrass factorization theorem]], there is an analogy to partial fraction expansions for certain meromorphic functions.
A proper rational function, i.e. one for which the [[degree of a polynomial|degree]] of the denominator is greater than the degree of the numerator, has a partial fraction expansion with no polynomial terms. Similarly, a meromorphic function ''f(z)'' for which |''f(z)''| goes to 0 as ''z'' goes to infinity at least as quickly as |''1/z''|, has an expansion with no polynomial terms.
==Calculation==
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