The theory of functions of one complex variable is one of the most central and fascinating chapters of mathematics. It has its prehistory with the works of Leonhard Euler (1707–1783), Joseph-Louis Lagrange (1736–1813), and Carl Friedrich Gauss (1777–1855), its gold period with Augustin-Louis Cauchy (1789–1857), G. F. Bernhard Riemann (1826–1866), Hermann Schwarz (1843–1921), and Karl Weierstrass (1815–1897), and it is the result of the contributions of many mathematicians in the period 1800–1950. The ideas, the methods, and the results of the theory of holomorphic functions play a fundamental role in several fields of mathematics both pure and applied, beyond their essential beauty. Here we shall limit ourselves to an elementary introduction
KeywordsHolomorphic Function Fundamental Theorem Laurent Series Residue Theorem Essential Singularity
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