>
> > Actually, we can not expand 'x*cos(1/x)' to UPS.
>
> What does that mean? I add a print expression to
> lseries := exprToGenUPS(fcn, ...),
> for "fcn := x*cos(1/x)", lseries is "cos(1/x)*x".
My point is that this is not a Lurent (or Puiseaux)
series. Here we have one term and coefficient before
'x' is 'cos(1/x)'. In particular coefficient depends
on 'x'. Since 'cos' is bounded this is good enough
to prove that 'x*cos(1/x)' tends to 0 when 'x'
thend to 0, but not much more.
In principle we could say that 'Si(1/x)' is its own
expansion (it is bounded so may appear as coefficient
befor 'x^0'), but this is of little use for the
computing limits. 'Si(x)' can be written as
of form 'c0 + cos(x)*f1 + sin(x)*f2' where both
'f1' and 'f2' have Lauren expansion at infinity.
So we can produce useful expansion of 'Si(1/x)'.
However, before going forward with this I would prefer
to look at big picture, in particular at Shackell
theory.
--
Waldek Hebisch
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