You are very right. The name TAYLOR is somewhat misleading. There is a
bug(fix) you should consider (applying) when using taylor together with
sums:
http://sourceforge.net/tracker/index.php?func=detail&aid=663873&group_id=4933&atid=104933
(well, the second of the two)
The following happens in unpatched maxima if you feed taylor with a sum
that contains the expansion variable as a limit:
(C1) taylor(sum(k,k,0,m),m,0,3);
(D1)/T/ k + . . .
Concerning extensions: The algolib group at inria developed software for
maple, it is certainly worth it to do the same for maxima. However, this
is maybe a demanding task.
http://algo.inria.fr/libraries/libraries.html#gdev
(you are into chemistry, not maths, aren't you?)
Martin
> 3. It seems that TAYLOR is somewhat more clever than the documentation
> would indicate. Consider:
>
> (C1) f(x):=1+1/x+exp(-x)*(1+1/x);
> 1 1
> (D1) f(x) := 1 + - + EXP(- x) (1 + -)
> x x
> (C2) taylor(f(x),x,inf,2);
> 1 1 - x
> (D2)/T/ 1 + - + . . . + (1 + - + . . .) %E + . . .
> x x
>
> This is neither a Taylor or Laurent series, but is very useful in
> assymptotic analysis of expressions. I don't know how robust this
> behavior is, for example:
>
> (C1) taylor(sin(x)/(1+x),x,inf,3);
> TAYLOR encountered an essential singularity in:
> SIN(x)
> -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
>
> Rather than giving an error, it might be nice to have the option of
> keeping the sin (or any other essentially singular function, like
> exp(-x)) explicit and taylor expanding the rest; i.e.,
>
> sin(x)/x -sin(x)/x**2 + ...
>
>
> In any event this behavior is undocumented.
>
> David
> _______________________________________________
> Maxima mailing list
> Maxima@www.math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>