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The results obtained thus far have been, for the most part, corollaries of Cauchy’s integral theorem on discs. In this chapter, we extend these results to holomorphic functions defined on arbitrary domains. On the one hand, the local theory will be applied in full; on the other, it will be completed by showing that the local theory in fact holds exclusively on simply connected domains.

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The Residue Theorem

  • 章节

  • 发表日期：

    2026年

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  • Norbert Steinmetz

摘要

The results obtained thus far have been, for the most part, corollaries of Cauchy’s integral theorem on discs. In this chapter, we extend these results to holomorphic functions defined on arbitrary domains. On the one hand, the local theory will be applied in full; on the other, it will be completed by showing that the local theory in fact holds exclusively on simply connected domains.