Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Complex Analysis Theorems of Complex analysis
Let f and g be two holomorphic functions on a domain \(D \subset \mathbb{C}\) . Assume f(z) = g(z) for all z in an infinite sequence {zn} converging to a point z0 in D. And it is given that f has a zero of order 3 at z0. Which of the following statement is true?
1
( g ) must also have a zero of order 3 at z0.
2
( g ) must have a zero at z0, but the order can be different from 3.
3
( g ) must have a zero of order at least 3 at z0 .
4
Nothing can be concluded about the zeros of ( g ) at z0 without additional information.
5
Question Not Attempted