Re: Confusing Result with Series

*To*: mathgroup at smc.vnet.net*Subject*: [mg121247] Re: Confusing Result with Series*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 6 Sep 2011 03:56:17 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109051105.HAA28332@smc.vnet.net>*Reply-to*: murray at math.umass.edu

In Mathematica 8.0.1, I'm seeing the same surprising result as you (albeit in ordinary OuputForm rather than the InputForm to which you converted the output) for Series[x/Sqrt[1 + Sqrt[x]], {x, 0, 1}] namely, including the term -(1/2) x^(3/2), which certainly has order greater than the requested 1. However, the result of Series[Sqrt[x^2/(1 + Sqrt[x])], {x, 0, 1}] is essentially what you expected, namely, x + O[x]^(3/2). Of course the two functions are NOT the same when, e.g., x < 0, although they are the same when x >= 0. Still, the behavior with the first version of the function does seem contrary to the documentation. Perhaps somebody here will tell us why it's not. Otherwise, I suggest you submit this directly to Wolfram Research as a bug. On 9/5/11 7:05 AM, jschwab wrote: > 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 > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Confusing Result with Series***From:*jschwab <jschwab@gmail.com>