hi Andrey
you wrote
>My question was is it possible operate with
> sums without trying to summate. Something like sum(f(i),i). And use them
> in integrals, series expansions and so on.
It's OK. Unless sum has inf in expression.
eample
(C1) plot2d(sum(1/(x+i)^3,1,10),[x,0,10]);
plot2d(sum(1/(x+i)^3,1,inf),[x,0,10]) is not executable.
Your problem can be solve,a is converged uniformally
So change order operator sum ,taylor.
(C1) taylor(1/(1+x+i)^3,x,0,5)$
(C2) a:sum(%,i,1,inf)$
(C3) changevar(a,i+1-n,n,i);
We obtain answer for your problem,
ZETA(3)-1 -3(ZETA(4)-1)*x + 6(ZETA(5)-1)*x^2
-10(ZETA(6)-1)*x^3+15(ZETA(7)-1)*x^4-21(ZETA(8)-1)*x^5
Too noun expression obtained,example
(C5) taylor(limit(sum(1/(x+i+1)^3,i,1,p),p,inf),x,0,5);
but exact calc may need to change order two operator,as (C1)~(C3)
thanks
Gosei Furuya (go_furuya@infoseek.jp)
>
> (C1) a:sum(1/(1+x+i)^3,i,1,inf);
>
> INF
> ====
> \ 1
> (D1) >------------
> / 3
> ====(x + i + 1)
> i = 1
> (C2) taylor(a,x,0,5);
>
> TAYLOR unable to expand at a point specified in:
> ERREXP1
> -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
>
> As I can see this is impossible.