Re: Bug with Series[] - help wanted

*To*: mathgroup at smc.vnet.net*Subject*: [mg65416] Re: [mg65394] Bug with Series[] - help wanted*From*: Bruce Miller <brucem at wolfram.com>*Date*: Fri, 31 Mar 2006 06:09:09 -0500 (EST)*References*: <200603301029.FAA18297@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The order notation O[1/r] is part of how the output of Series is formatted. It does not closely correspond to the internal form of a series. In[1]:= $VersionNumber Out[1]= 5.2 In[2]:= s=Series[1/(r+1), {r, Infinity,3}] Out[2]= 1 -2 -3 1 4 - - r + r + O[-] r r Look at the internal structure of the Series output: In[3]:= FullForm[s] Out[3]//FullForm= SeriesData[r, DirectedInfinity[1], List[1, -1, 1], 1, 4, 1] Turn it into a polynomial. Note that the O term goes away. In[4]:= Normal[s] Out[4]= -3 -2 1 r - r + - r In[5]:= FullForm[%] Out[5]//FullForm= Plus[Power[r, -3], Times[-1, Power[r, -2]], Power[r, -1]] I hope this is helpful. Bruce Miller Technical Support Wolfram Research, Inc. support at wolfram.com On Mar 30, 2006, at 4:29 AM, GidiL wrote: > Hello all! > > I would really appreciate some help. > > Mathematica has a built-in function called Series: > Series[x,x_0,n], > which allows to expand functions into power series where x is the > variable, x_0 is the point about which we expand, and n is the desired > order of expansion. > > It also allows x_0 to be infinity, which is very useful when one needs > multiple expansion (as in gravitational waves and electromagnetic > radiation). > > Although is allows to expand series in terms of 1/x and writes O(1/x) > (and its powers) in the output, it does not allow this to be entered in > the input. To convince yourselves, try it out. Enter in the input, > e.g., 1+ 1/r+ (O(1/r))^2, and it will tell you that 1/r is not a > variable. > > If, on the other hand, you entered: > In=Series[1/(r+1), {r, Infinity,3}]//Simplify > you will get > Out=1/r-(1/r)^2+(1/r)^3+(O(1/r))^4 > > which shows that the output is possible, but the input is impossible. > > Can anyone offer some assistance? > > Thanks, > Gideon

**References**:**Bug with Series[] - help wanted***From:*"GidiL" <gidienator@gmail.com>