Calculating Pole Order: Is Infinity Possible?

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SUMMARY

The discussion centers on the calculation of pole order in complex functions, specifically addressing the question of whether a pole can have infinite order. The consensus is that while poles can have finite orders, the concept of an infinite order pole is not applicable in practical scenarios. The participant identified a mistake in their calculations related to the Taylor expansion of the sine function, which clarified their understanding of pole orders.

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I'm calculating the order of a pole of some function and I'm wondering: is it possible that a pole has order infinity?
 
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Not in real life. What's the context?
 
I found my mistake. Had to rewrite a sin in a taylor expansion...
 

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