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Partial Fractions in Complex Analysis
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Geliefert zwischen Mi., 26.11.2025 und Do., 27.11.2025
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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 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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131259463
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Genre Physik & Astronomie
- Größe H220mm x B220mm
- EAN 9786131259463
- Format Fachbuch
- Titel Partial Fractions in Complex Analysis
- Herausgeber Betascript Publishing
- Anzahl Seiten 96
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