Re: trig asymptotics

• To: mathgroup at smc.vnet.net
• Subject: [mg18433] Re: [mg15583] trig asymptotics
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Wed, 7 Jul 1999 00:11:22 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```
Series[1/2*ArcTan[1/x]*ArcSinh[1/x], {x, 0, 1}] /. x -> 1/n

or, if you prefer

In[4]:=
Normal[Series[1/2*ArcTan[1/x]*ArcSinh[1/x], {x, 0, 1}] /. x ->
1/n]//PowerExpand
Out[4]=
-Log[2] - Log[n]   1
---------------- + - Pi (Log[2] + Log[n])
2 n          4
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: Arnold Knopfmacher <arnoldk at gauss.cam.wits.ac.za>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg18433] [mg15583] trig asymptotics
>Date: Thu, Jan 28, 1999, 6:23 PM
>

> Hi All
>
> 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..
>
> The output I expect is
> (Log[n]+Log[2]) Pi/4 -(Log[2]/2+Log[n]/2)/n +O[1/n^2]. Thank you
>
> Arnold Knopfmacher
> Wiwwatersrand University
>

```

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