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What is 3 Meromorphic functions about?

This chapter is divided into two parts, the classical theory of meromorphic functions prior to the work of Rolf Nevanlinna (1895-1980) and the work that followed. The entire landscape changed in a profound way in 1925 with the work of the latter, and in subsequent years that of his student Lars Ahlfors (1907-1996). Classical theory Meromorphic functions are analytic with the exception of poles. It is certainly the case that in the domain where a function is meromorphic, the poles have no accumulation point for if they did, then the accumulation point would be a singularity, which is clearly not a pole due to the Laurent series expansion. A simple consequence of this is the following:3.1 Theorem. Any meromorphic function f (z) in the complex plane C is the quotient of two entire functions having no common zeros.Indeed, this was just Theorem 2.3 derived as a consequence of the Weierstrass product theorem and an example of the interaction between entire and meromorphic functions. Laurent series Recall that an analytic function f (z) on a domain Ω ⊆ C with a pole of order m j at a point b j can be expressed by the Laurent serieswhere r is the distance from b j to the next nearest pole

Publisher

De Gruyter

Published

2022

Language

EN