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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 ]


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