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Re: Compute ArcTan(n Pi+ Pi/2 + O(1))

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95902] Re: Compute ArcTan(n Pi+ Pi/2 + O(1))
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Thu, 29 Jan 2009 05:57:38 -0500 (EST)
  • References: <glpfdv$kje$1@smc.vnet.net>

On 28 =C9=E1=ED, 13:26, Franc... at news.free.fr, Fay... at news.free.fr wrote:
> Hello,
>
> I'm new to Mathematica and I want to compute a serie expantion of
>
> ArcTan(n Pi + Pi/2 + O(1))   (The O is a big O and is taken when n goes
> to Infinity)
>
> I dont know how to input O(1) in Mathematica. For example
> O[n,Infinity]^0 simplifies to 1 which is not what I want.
>
> Thanks for the help.
> Francois

O(1) in Mathematica is O[x]^1.

So for exaple

In[5]:= ArcTan[n*Pi + Pi/2 + O[n]^1] // InputForm

Out[5]//InputForm=
SeriesData[n, 0, {ArcTan[Pi/2]}, 0, 1, 1]

In[6]:= ArcTan[n*Pi + Pi/2 + O[n]^3] // InputForm

Out[6]//InputForm=
SeriesData[n, 0, {ArcTan[Pi/2], (4*Pi)/(4 + Pi^2), -Pi^3/(2*(1 +
Pi^2/4)^2)}, 0, 3, 1]

etc

Dimitris


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