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

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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