Re: trig asymptotics
- To: mathgroup at smc.vnet.net
- Subject: [mg15635] Re: [mg15583] trig asymptotics
- From: "Richard Finley" <rfinley at medicine.umsmed.edu>
- Date: Sat, 30 Jan 1999 04:28:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello Arnold
ans = TrigToExp[ ArcTan[x] ArcSinh[x]/2] /. x -> 1/n
Series[ ans, {n,0,1}] /.n->1/n
Out = Pi/4 (Log[2] + Log[n]) - ( Log[2] + Log[n] ) /(2 n) + O[1/n^2]
regards....RF
>>> Arnold Knopfmacher <arnoldk at gauss.cam.wits.ac.za> 01/28/99 03:23AM >>>
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