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Re: trig asymptotics

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  • Subject: [mg15635] Re: [mg15583] trig asymptotics
  • From: "Richard Finley" <rfinley at>
  • Date: Sat, 30 Jan 1999 04:28:34 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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]


>>> Arnold Knopfmacher <arnoldk at> 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

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