> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Barton Willis
> Sent: Friday, September 29, 2006 4:42 AM
> To: maxima at math.utexas.edu
> Subject: adding facts to taylor
>
>
> Does anybody understand the taylor code (hayat.lisp) well
> enough to tell me how to add a fact such as A&S 6.5.32 (see
> http://www.math.sfu.ca/~cbm/aands/page_263.htm)?
> Since 6.5.32 isn't 100% a power series, maybe it isn't
> reasonable to expect taylor to handle it, I suppose.
The original author of that code was Richard Zippel, who now works for Sun
Microsystems.
I think it is unreasonable to expect taylor() to handle asymptotic series
generally...
The Taylor series package (apparently "hayat" is tailor in Hebrew...)
is an implementation of a kind of algebra known as FPS (formal power
series), in which one can add/multiply/compose objects. Also divide by
some, but not all, series, and revert.
While we may identify FPS with taylor series, FPS does not refer in any way
to notions of convergence, at least as far as I know.
Anyway, an asymptotic series is not a FPS, so it would not be likely to fit
in.
People have talked about computing asymptotic expansions for many years,
including for example, the 1971 first paper on Macsyma,in which there is an
example of computing a series, and a book by Rand on asymptotic series and
Macsyma. This tends to be a messy business -- before one can automate a
procedure, it has to be understood well enough to automate, and except for
bits here and there, much of the asymptotic series generation is ad hoc.
RJF
>
> I have some code for the incomplete gamma function.
> The taylor function works okay for things like
> taylor(incomplete_gamma(a,x),x,1,5), but it fails for
> taylor(incomplete_gamma(a,x),x,inf,5).
>
> Barton
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