How to prove that this two functions have simple poles:

at

at where k is an integer

Regards.

Printable View

- May 12th 2011, 05:01 AMhurzProving the simple poles
How to prove that this two functions have simple poles:

at

at where k is an integer

Regards. - May 12th 2011, 05:04 AMHallsofIvy
Well, what is the

**definition**of "simple pole"? - May 12th 2011, 05:12 AMhurz
you have a simple pole when the maximum power of 1/z you have is 1 in the laurent series of the function

- May 12th 2011, 09:40 AMjamesdt
I'm not sure I understood your definition of a 'simple pole'. Is not a pole commonly defined as the values of such that the denominator is zero? And perhaps by simple, you mean that the pole has multiplicity one?

For example, the first function would have a pole when , or equivalently . Then certainly is a pole, but since is periodic, there most certainly are other poles also.