Suppose that a function f is meromorphic in the domain D
Chapter 0, Problem 7.44(choose chapter or problem)
Suppose that a function f is meromorphic in the domain D interior lo a simple closed contour Con which f is analytic and nonzero. and let Do denote the domain consisting of all points in D except for poles. Point out how it follows from the lemma in Sec. 28 and Exercise 11. St..'C. 83. that if f (:) is not identically equal to zero in Do. then the zeros off in D arc al I of ti ni tc order and that they are ti nitc in number. Suggesr imr: :'\ote that if a point : 0 in D is a zero of .f that is not of ti ni te order. then there must be a neighborhood of : 0 throughout \Vhich f (:.) is identically equal to zero.
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