shortly we can derive the Cauchy's residue theorem (its general form) just by direct integration of a Taylor series placing an open curve onto a specific domain, in order to satisfy holomorphic properties
Pagano, F. (2022). Pagano's theorem (short proof of generalized cauchy residue theorem). Afribary. Retrieved from https://afribary.com/works/pagano-s-theorem-short-proof-of-generalized-cauchy-residue-theorem
Pagano, Federico "Pagano's theorem (short proof of generalized cauchy residue theorem)" Afribary. Afribary, 11 Oct. 2022, https://afribary.com/works/pagano-s-theorem-short-proof-of-generalized-cauchy-residue-theorem. Accessed 11 May. 2024.
Pagano, Federico . "Pagano's theorem (short proof of generalized cauchy residue theorem)". Afribary, Afribary, 11 Oct. 2022. Web. 11 May. 2024. < https://afribary.com/works/pagano-s-theorem-short-proof-of-generalized-cauchy-residue-theorem >.
Pagano, Federico . "Pagano's theorem (short proof of generalized cauchy residue theorem)" Afribary (2022). Accessed May 11, 2024. https://afribary.com/works/pagano-s-theorem-short-proof-of-generalized-cauchy-residue-theorem