Here is a quirk discovered by a colleague:
asympt does not seem to honour the Order setting the ﬁrst time it is called for a particular expression:
Series expansion for large r converted to an algebraic expression. Note that Order is ignored.
I think this is well described as a ’quirk’; Maple seems to need to do one series expansion of the expression before it starts to honour the value of Order. If you skip/execute the a0 line below then the a1 line ignores/honours the Order option. If you cange the - in the a0 line to +, it works diﬀerently, so it seems to be something to do with remembering the series for that particular expression.
Without executing the a0 line we get:
This is not a great problem, but I am intrigued as to why it happens, and if there is a better anser than ’do it twice’
This is actually a bug in ”series” (which ”asympt” calls). I don’t have any advice other than to call it twice. The reason it works the second time, I think, is that ”series” consults its remember table to see if it has computed the same series before to this or higher order; if it has done so, it truncates the series appropriately.