Abstract
As early as the 18th century many real integrals were evaluated by passing up from the real domain to the complex (passage du réel á l’imaginaire). Especially Euler (Calcul intégrat), Legendre (Exercices de Calcul Intégral) and Laplace made use of this method at a time when the theory of the complex numbers had not yet been rigorously grounded and “all convergence questions still lay under a thick fog.” The attempt to put this procedure on a secure foundation lead Cauchy to the residue calculus.
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© 1991 Springer Science+Business Media New York
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Remmert, R. (1991). The Residue Calculus. In: Theory of Complex Functions. Graduate in Texts Mathematics, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0939-3_15
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DOI: https://doi.org/10.1007/978-1-4612-0939-3_15
Publisher Name: Springer, New York, NY
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