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The Complex Logarithm
Автор: Mike, the Mathematician
Загружено: 2025-04-12
Просмотров: 670
Описание:
We discuss the holomorphic inverse of the exponential function. Since the exponential function is 2(pi)i periodic, the inverse function will be a multivalued function which jumps as the argument changes by 2(pi)i. We then use this idea to define a branch of the logarithm which is one of the multivalued outputs which is holomorphic on an open connected set and is continuous. We define the principal branch of the logarithm which we will use extensively.
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #logarithm
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