All zeros of an analytic function are isolated if the function is not identically zero.

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Here I discussed a theroem related to zeros of an analytic function.
Reference: Complex Analysis by S.Arumugam, A,Thangapandi Issac and A.Somasundaram.

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  1. Subathra
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I have doubt by the identity theorem set of zeros of an analytic function has a limit point then f is identically 0
f(Z)= (Z-a) ^m(Z-b)^n Set of zeros are a and b . S={a, b} this is the zeros of the set. This set S has limit point?

Ramanarajacademy
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Suppose f(Z)= (Z-a)^n a is zero of order n
Neighborhood of a contains no other Zeros that is ( a-s, a+s) contains zero a only. Is it correct

Ramanarajacademy