Re: Asymptotic expansions
- To: mathgroup at smc.vnet.net
- Subject: [mg14302] Re: Asymptotic expansions
- From: graciark at ippt.gov.pl (Adam Ciarkowski)
- Date: Tue, 13 Oct 1998 01:21:18 -0400
- Organization: IPPT PAN
- References: <6vhje4$jga@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <6vhje4$jga at smc.vnet.net>, phpcp at csv.warwick.ac.uk says...
>
>
>Hi!
>
>Can someone help me get asymptotic expansions of the special functions
>using Mathematica?
>
>cheers.
>
>
In case of simple expansions in powers of the expansion parameter, Series
command may be used. For example, one can varify validity of the Stirling's
formula with:
Series[Gamma[z], {z, 2, Infinity}].
In general, however, some preparatory mathematical steps are first needed to
formulate the problem in such a way, that appropriate asymptotic approach can
be used. Usually, it is advisable to represent the special function in terms of a
suitable integral, for which a variety of asymptotic methods is available:
integration by parts, Watson's lemma, saddle point method, etc. Those methods
can be translated into Mathematica language.
For more constructive answer specific information concerning the expanded
function and the type of asymptotic expansion sought is needed.
Greetings,
Adam
........
(remove gr from my e-mail address)