Two Theorems of Cauchy

Norbert Steinmetz ()
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Norbert Steinmetz: TU Dortmund, Department of Mathematics

Chapter 2 in Lectures on Complex Analysis, 2026, pp 29-57 from Springer

Abstract: Abstract 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.

Date: 2026
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DOI: 10.1007/978-3-032-13996-2_2

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