When Did the Concept of Residue in Complex Analysis Emerge?

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The concept of residue in complex analysis emerged from the foundational work of mathematicians such as Jean-le-Rond d'Alembert and Augustin-Louis Cauchy in the 18th and 19th centuries. Their studies on wave propagation led to significant mathematical discoveries, including Cauchy's integral theorem, which laid the groundwork for the formal definition of residues. This concept became essential for evaluating complex integrals and understanding singularities in complex functions.

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Please anyone tell me about when, why and how did the concept of residue in complex analysis started?
 
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Jean-le-Rond d'Alambert and Augustine Cauchy (and some others) made extensive studies of wave propagation along with fundamental mathematical discoveries relating to limits, continuity and covergence. Cauchy's integral theorem was one product of their investigations.
 

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