Re: trig asymptotics
- To: mathgroup at smc.vnet.net
- Subject: [mg15654] Re: trig asymptotics
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Sat, 30 Jan 1999 04:28:48 -0500 (EST)
- Organization: University of Western Australia
- References: <78pabu$cs9@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Arnold Knopfmacher wrote:
> How do I get an asymptotic expansion for large n of the function (1/2)
> ArcTan[n] ArcSinh[n]? The command
>
> Series[(1/2) ArcTan[n] ArcSinh[n], {n, Infinity, 2}] does not work..
I have reported this is a bug.
> The output I expect is
> (Log[n]+Log[2]) Pi/4 -(Log[2]/2+Log[n]/2)/n +O[1/n^2].
You can get the result you are after by combining two separate
asymptotic Series manually(output supressed),
In[1]:= Series[ ArcTan[n] , {n, Infinity, 2}] In[2]:= Series[ ArcSinh[n]
, {n, Infinity, 2}] In[3]:= Series[1/2 Normal[%]Normal[%%], {n,
Infinity, 2}] //
PowerExpand // Simplify
The use of PowerExpand should be ok in this case to get the answer close
to the form you desire.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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