Question

63. If the principal part contains an infinite number of non-zero terms of (z-a) then z=a is known as
O A. Poles
O B. Isolated Singularity
O C. Essential Singularity
O D. Removable Singularity​

Answer 1

option (c) is your answer..

C. Essential Singularity

Answer 2

If the principal part contains an infinite number of non-zero terms of (z-a) then z=a is known as Essential Singularity (Option C)

Explanation:

• According to the behavior of the function in a deleted neighborhood of the point concerned, Isolated singularities are divided into three types:
• Removable singularity, if   $lim_{z \to \aa f(z)$ f (z) exists finitely.
• Pole
• Essential singularity, f (z) does not tend to a limit (finite or infinite) as $z-a$