Hello,
> Hi,
>
> consider the following:
>
> ,----
> | Maxima 5.9.0 http://maxima.sourceforge.net
> | Distributed under the GNU Public License. See the file COPYING.
> | Dedicated to the memory of William Schelter.
> | This is a development version of Maxima. The function bug_report()
> | provides bug reporting information.
> | (C1) gradef(cir(x), (cos(x)-1)/x) $
> |
> | (C2) tellsimp(cir(0), %gamma) $
> |
> | (C3) limit(diff(cir(x), x, 0), x, 0);
> |
> | (D3) %GAMMA
> | (C4) limit(diff(cir(x), x, 1), x, 0);
> |
> | (D4) 0
> | (C5) limit(diff(cir(x), x, 2), x, 0);
> |
> | 1
> | (D5) - -
> | 2
> | (C6) limit(diff(cir(x), x, 3), x, 0);
> |
> | (D6) 0
> | (C7) taylor(cir(x), x, 0, 3);
> |
> | TAYLOR encountered an unfamiliar singularity in:
> | cir(x)
> | -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
> `----
>
> So apparently all the information necessary to get the Taylor series
> is there, but TAYLOR presumably does not take the limit but seems to try
> evaluating the n-th derivative with x set to 0.
I think, there aren't a problem with Maxima. The cir(x) function is defined in 0, but the functions derivates isn't defined in 0, as
(Cos(x)-1)/x, although the limits (for left and right) exists (remember continuity conditions). Therefore the cir(x) function cannot
be represented in Taylor Series, because coefficients An, is given in terms of function derivates. Think in the Laurent Series !!!
Bye,
Juan Pablo
> I can, of course, build the desired expansion easily myself, but is
> there some switch to make TAYLOR or some other function produce it?
> I haven't found anything in the docs.
>
> TIA,
>
> Albert.
>
> _______________________________________________
> Maxima mailing list
> Maxima@www.math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
--
______________________________________________
Check out the latest SMS services @ http://www.linuxmail.org
This allows you to send and receive SMS through your mailbox.
Powered by Outblaze