Abstract
Differentiation and integration of complex functions are significantly different from those of real functions. In this chapter, we show that two very important theorems—the Cauchy theorem (Sect. 7.2.2) and the Taylor series expansion (Sect. 7.4.3)—result in a broad range of mathematical consequences that are highly relevant and useful in mathematical physics. However, before moving on to the principal discussion, we deal with the underlying concepts of analytic functions (Sect. 7.1.2) and the geometric meaning of analyticity (Sect. 7.1.5).
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© 2009 Springer-Verlag Berlin Heidelberg
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Shima, H., Nakayama, T. (2009). Complex Functions. In: Higher Mathematics for Physics and Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b138494_7
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DOI: https://doi.org/10.1007/b138494_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87863-6
Online ISBN: 978-3-540-87864-3
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