This (message below) answers one of my questions I didn't ask. (thanks!)
Well, to answer my other question I just found out that maxima doesn't
care much about analyticity:
(C1) sum(n!*x^n,n,0,INF);
INF
====
\ n
(D1) > n! x
/
====
n = 0
(C2) taylor(sum(n!*x^n,n,0,INF),x,0,3);
2 3
(D2)/T/ 1 + x + 2 x + 6 x + . . .
I'm not sure(!) whether this is a good thing. It might come in handy, it
might be dangerous.
In any case, I think that the documentation of TAYLOR is misleading, it
says
expands the expression exp in a truncated Taylor series (or Laurent
series, if required) in the variable var around the point pt.
which is not true. It is more like
computes a truncated series expansion of exp, with respect to the
variable var, about the point pt, up to order pow.
(note that Maple distinguishes between "taylor", "series" and "tpsform",
the last taking a formal power series...)
Martin
On 25 Jan 2003, Wolfgang Jenkner wrote:
> Daniel Duparc <daniel.duparc@free.fr> writes:
>
> > I have another problem: I don't know how
> > to use the function "revert" described
> > in this chapter(e.g. how to invert the
> > Taylor series of sin(x)).
>
> (C1) bothcases:false$
> (C2) load("revert");
> (D2) /usr/share/maxima/5.9.0.rc4/share/calculus/revert.mac
> (C3) revert(taylor(sin(x),x,0,7),x);
> 7 5 3
> 75 X + 126 X + 280 X + 1680 X
> (D3)/R/ --------------------------------
> 1680
> (C4) distrib(%);
> 7 5 3
> 5 X 3 X X
> (D4) ---- + ---- + -- + X
> 112 40 6
> (C5) taylor(asin(x),x,0,7);
> 3 5 7
> X 3 X 5 X
> (D5)/T/ X + -- + ---- + ---- + . . .
> 6 40 112
> (C6)
>
> The explanation is... no, no sermon on case-sensitivity this time :-)
> As an alternative, you could dispense with setting BOTHCASES to FALSE
> by converting all of revert.mac to uppercase.
>
> Wolfgang
>
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