Re: Asymptotic expansions
- To: mathgroup at smc.vnet.net
- Subject: [mg14300] Re: Asymptotic expansions
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 13 Oct 1998 01:21:16 -0400
- Organization: University of Western Australia
- References: <6vhje4$jga@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
phpcp at csv.warwick.ac.uk wrote:
> Can someone help me get asymptotic expansions of the special functions
> using Mathematica?
Several asymptotic expansions of special functions are built in. For
example, try
Series[Gamma[x],{x,Infinity,2}]
A search of comp.soft-sys.math.mathematica using Deja news
http://www.dejanews.com/home_ps.shtml
for asymptotic returns a number of postings related to this topic so you
might want to follow up on these threads. For example,
Arnold Knopfmacher wrote:
> Can anyone tell me how to get asymptotic expansions in
> Mathematica. For example I would like to ask what is
> (1+1/n)^n +O(1/n^2) and get back an asymptotic result like
> Exp[1-1/(2n)]+O[1/n^2].
Here is one way:
In[1]:= Exp[Series[n*Log[1 + 1/n], {n, Infinity, 2}]]
Out[1]=
E 1 2
E - --- + O[-]
2 n n
There are many subtleties in dealing with asymptotic expansions. What
functions are you after?
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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