Question: The Series function

The image is an extract from the help page on the function "series" my question is in regard to how a method is selected, ie either it be a taylor or laurent series expansion, or as it defines in the passage attached "a more generalised series".

im just curious to know what procedure maple uses to make this choice when the series function is called, and im also finding it hard to replicate and understand the procedure of computing coeffiecents as described in the extract for a generalised series.

 

Thanks.
 

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