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Argument principle
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==History== According to the book by [[Frank Smithies]] (''Cauchy and the Creation of Complex Function Theory'', Cambridge University Press, 1997, p. 177), [[Augustin-Louis Cauchy]] presented a theorem similar to the above on 27 November 1831, during his self-imposed exile in Turin (then capital of the Kingdom of Piedmont-Sardinia) away from France. However, according to this book, only zeroes were mentioned, not poles. This theorem by Cauchy was only published many years later in 1874 in a hand-written form and so is quite difficult to read. Cauchy published a paper with a discussion on both zeroes and poles in 1855, two years before his death.
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