I wasn't able to solve the problem using your tip.

Here's what I've done :

Considering the singularity at

, the series expansion of

around this singularity (singularity for

) is

where

so

.

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I've a side-note question : From this can I conclude that the order of the pole of

when

is 2?

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Now I wrote that the pole of

occurs when

has a zero. That is, when

. I go nowhere.

No let me try again you way :

.

For

, the limit is worth

. Does that mean the order of the pole of

at

is

, and that I've successfully solved the exercise?