Further Topics

Abstract

In this section we examine an integral that in effect counts the number of poles and zeros of a meromorphic function f. Recall that, if f has Laurent series $\sum\nolimits_{n = - \infty }^\infty {{a_n}} {(z - c)^n}$ at c, then ord(f,c) = min {n: a _n ≠ 0}. If ord(f,c) = m > 0 then f(c) = 0, and we say that c is a zero of order m of the function f. If ord(f,c) = -m < 0, then c is a pole of order m.