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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