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In this chapter, local versions of Cauchy’s integral theorem and integral formula are established. These theorems form the cornerstones of complex analysis and give rise to a wealth of applications. Key topics include holomorphic parameter integrals, power series expansions of holomorphic functions, the fundamental theorem of algebra, isolated singularities, the Poisson integral formula and the foundations of holomorphic functions in several complex variables.

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Two Theorems of Cauchy

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  • 发表日期：

    2026年

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  • Norbert Steinmetz

摘要

In this chapter, local versions of Cauchy’s integral theorem and integral formula are established. These theorems form the cornerstones of complex analysis and give rise to a wealth of applications. Key topics include holomorphic parameter integrals, power series expansions of holomorphic functions, the fundamental theorem of algebra, isolated singularities, the Poisson integral formula and the foundations of holomorphic functions in several complex variables.