Abstract
One of the most powerful tools made available by complex analysis is the theory of residues, which makes possible the routine evaluation of certain definite integrals that are impossible to calculate otherwise. The derivation, application, and analysis of this tool constitute the main focus of this chapter. In the preceding chapter we saw examples in which integrals were related to expansion coefficients of Laurent series. Here we will develop a systematic way of evaluating both real and complex integrals.
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The limit is taken because in many cases the mere substitution of z 0 may result in an indeterminate form.
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Provided that Jordan’s lemma holds there.
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© 2013 Springer International Publishing Switzerland
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Hassani, S. (2013). Calculus of Residues. In: Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01195-0_11
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DOI: https://doi.org/10.1007/978-3-319-01195-0_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01194-3
Online ISBN: 978-3-319-01195-0
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