Cauchy-Riemann equations are of basic importance in the theory of analytic functions and its applications to problems of physics and engineering. However, is should be noted that these equations had already been studied in the 18th century by D'Alembert and Euler, in researches devoted to the application of functions of one complex variable to hydrodynamics (D'Alembert and Euler), and to cartography and integral calculus (Euler).[1]
Holomorphic Functions v.s. Analytic Functions
Holomorphic, entire functions, complex differentiable, holomorphic functions and analytic functions