Bug or limitation in Series?
- To: mathgroup at smc.vnet.net
- Subject: [mg119911] Bug or limitation in Series?
- From: Dushan Mitrovich <dushanm at nnips.net>
- Date: Wed, 29 Jun 2011 05:28:53 -0400 (EDT)
Just ran into a result that surprised me:
In[1]:= Series[(1 + u/Sqrt[u^2 + v^2]), {u, -\[Infinity], 4},
Assumptions -> {u \[Element] Reals, v \[Element] Reals}]
Out[1]:= 2 - v^2/(2 u^2) + (3 v^4)/(8 u^4) + O[1/u]^5
which is not correct. This produces the correct result:
In[2]:= Series[(1 - u/Sqrt[u^2 + v^2]), {u, \[Infinity], 4},
Assumptions -> {u \[Element] Reals, v \[Element] Reals}]
Out[2]:= v^2/(2 u^2) - (3 v^4)/(8 u^4) + O[1/u]^5
The documentation says that Series can produce appropriate series about
\[Infinity], but says nothing about -\[Infinity], so I guess it's not
really doing anything counter to what's claimed.
Still, it surprised me that so basic an operation should produce a wrong
result. In a more complicated case that hadn't first been worked out by
hand, one might have been led quite a ways along a path of nonsense.
Should this be considered a bug, or a limitation? If the latter, it
might be a good idea to have the documentation warn of this pitfall.
- Dushan
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