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 [ reverse the middle word of address to reply ]