Entire and Meromorphic Functions

Abstract

A function is said to be entire if it is analytic on all of C. It is said to be meromorphic if it is analytic except for isolated singularities which are poles. In this chapter we describe such functions more closely. We develop a multiplicative theory for entire functions, giving factorizations for them in terms of their zeros, just as a polynomial factors into linear factors determined by its zeros. We develop an additive theory for meromorphic functions, in terms of their principal part (polar part) at the poles.