lim h→0 f(z + h)− f(z) h if this limit exists. If the derivative of f exists at z, we denote its value by f ′(z), and we say f isholomorphic at z. If f is holomorphic at every point of an open set U we say that f is holomorphic on U . This definition naturally leads to several basic remarks. First, the definition formally looks identical to the limit definition of a derivative of a function of ...