Entire and Meromorphic Functions

Abstract

The works by Weierstrass, Mittag-Leffler and Picard dated back to the seventies of the last century marked the beginning of systematic studies of the theory of entire and meromorphicl functions. The theorems by Weierstrass and Mittag-Leffler gave a general description of the structure of entire and meromorphic functions. The representation of entire functions as an infinite product by Weierstrass served as the basis for studying properties of entire and meromorphic functions. The Picard theorem initiated the theory of value distribution of meromorphic functions. In 1899 Jensen proved a formula which relates the number of zeros of an entire function in a disk with the magnitude of its modulus on the circle. The Jensen formula was of a great importance for the development of the theory of entire and meromorphic functions.