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

**Follow-Ups**:**Re: Confusing Result with Series***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Confusing Result with Series***From:*Murray Eisenberg <murray@math.umass.edu>