Maxima] numerical summation of series, rational case.

Thanks!

Unfornutately I could not test it yet since my maxima balks at the :list
construct. Am I doing something wrong?

Michel
> * sumninf(a(n),p)  computes an approximate value of 
> sum(a(n),n,1,inf) with a(n) a rational function.
>
> It accelerate the convergence rate of a(n): 
> there is b(n) such that lim a(n)/b(n) = 1 then
>
> a(n) - b(n) converges to zero more quickly than a(n) and 
> sum(b(n),n,1,inf)  known.
>
> Repeating this procedure we speed up the covergence rate,
>  p is the number of times we speed up a(n).
>
> Finally sum(a(n),1,inf) = sum(a(n),1,20) + sum(a(n),20,inf)
>  aprox
> sum(a(n),n,1,20)+ sum(b(n),n,20,inf)
> because r(n) =  a(n) - b(n) converges very quickly to zero
>  this procedure  gives a good approximation.  */
>
> --source code -------------------------------------------
>
> :lisp (defun principal(ex) 
> (let* ((num (cadr ex)) (den (cddr ex)) (c1) (c2 (third den))
>  (deg) (g2 (second den)))
> (if (atom  num)  (setq c1  num g1 0) 
> (setq c1  (third num) g1 (second num)))
> (setq deg (- g2 g1))  (list '(MLIST SIMP) c1 c2 deg))) ;
>
> g1(ex):= block([l],l:?principal(rat(ex)), ex -
> l[1]/l[2]*product(1/(n+i),i,0,l[3]-1));
>
> matchdeclare(x_,integerp);
>
> defrule(uno,1/(n+x_),sum(-1/k,k,1,x_+20));
>
>
> sumninf(ex0,p):=block([ex],ex:rat(ex0),
> 	for i:1 thru p do ex:g1(ex),
> 	sum(ex0,n,1,20)+
>             apply1(partfrac(ex0 - ex,n),uno));