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Confusing Result with Series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121223] Confusing Result with Series
  • From: jschwab <jschwab at gmail.com>
  • Date: Mon, 5 Sep 2011 07:05:25 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi Mathematica Gurus,

I am seeing confusing behavior with the Series command, using
Mathematica 7.0.1 on Mac OS X.
Specifically, it is not always truncating at the order I would expect.
Here's a a simple example of the problem I'm having.

I expect that the result of a a series expansion of
\frac{x}{\sqrt{1 + \sqrt{x}}}
to first order will be
x + O(x^{3/2})
no matter how I write the input.

Instead, I see the following behavior.

In[175]:= Series[x/Sqrt[1 + Sqrt[x]], {x, 0, 1}]
Out[175]= SeriesData[x, 0, {1, Rational[-1, 2]}, 2, 4, 2]

In[176]:= Series[Sqrt[x^2/(1 + Sqrt[x])], {x, 0, 1}]
Out[176]= SeriesData[x, 0, {1}, 2, 3, 2]

Is this a known issue? Or some sort of expected behavior that I
haven't understood?
A naive Google search didn't reveal anything of particular relevance.

Thanks,
Josiah




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