hi Andrey
you wrote
> (C1) a:sum(exp(-(i+x)^(-2)),i,0,inf);
>
> 1
> INF - --------
> ==== 2
> \ (x + i)
> (D1) >%E
> /
> ====
> i = 0
> (C2) taylor(a,x,0,5);
>
> 1
> - --
> 2
> x
> (D2)/T/ %E + . . .
> (C3) taylor(a,x,0,10);
>
> TAYLOR unable to expand at a point specified in:
> ERREXP1
> -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
>
> It seems that expression (D2) is wrong.
for all fixed integer n>0,x->+0,Limit(%E^(-1/x^2)/x^n)is 0.
So,for all m,f(x):=%E^(-1/x^2),diff(f(x),x,m) is 0 at this point.
f(x) has not Taylor expansion at x=0.
As a matter of course, your (C2)has not effective Taylor expansion at x=0.
at (C1) you shoud rewrite i=1 from i=0.
But maxima can not taylor at x=0 because of sum(....,inf).
According your purpose,you write your new taylor with Maxima or
a(n+1)-a(n)=f(x+1),laplace or Ztransform shoud be test,I think.
thanks.
Gosei Furuya (go_furuya@infoseek.jp)