Question

If an entire function has a pole of order 5 at infinity then it is a polynomial of degree

Answer 1

Step-by-step explanation:

I need to show that if f is an entire function it has a pole at infinity if and only if it is a polynomial. If I start with a polynomial, it is easy ...

Answer 2

Concept

The polynomial P(z) = anz^n+· · ·+a0 s not equal to 0 has pole of order n at infinity. In fact, on the contrary, always the entire function

p(z) with a pole of order n at infinity is a polynomial of degree n.

This follows from Cacuha's estimates.

Given

It is given that an entire function has a pole of order 5 at infinity

Find

We need to find the degree of a polynomial

Solution

A polynomial with a pole of order n at infinity is a polynomial of degree n.

Here the function has a pole of order 5

n= 5 is given

Hence the polynomial is of degree 5

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