Partial Fractions in Complex Analysis
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In complex analysis, a partial fraction expansion is a way of writing a meromorphic function f(z) as an infinite sum of rational functions and polynomials. When f(z) is a rational function, this reduces to the usual method of partial fractions. 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)k + p(z), where a and b are complex, k is an integer, and p(z) is...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In complex analysis, a partial fraction expansion is a way of writing a meromorphic function f(z) as an infinite sum of rational functions and polynomials. When f(z) is a rational function, this reduces to the usual method of partial fractions. 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)k + 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 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.
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