The small set of functions from
loadfile(nusum,?>,dsk,share)
is, I believe, a decision procedure for indefinite (i.e. FINITE)
hypergeometric summation. Restrictions:
1) Both the summand and the answer must be expressible as products
of nth pwrs, factorials, binomials, and rational fcns.
Examples:
nusum(n*n!,n,0,n); ==> (n+1)! - 1
nusum(n^4*4^n/binomial(2*n,n),n,0,n); ==>
unsum(%,n); ==> n^4*4^n/binomial(2*n,n)
etc.
(UNSUM was formerly called DELTA, and is just the first backward
difference w.r.t. its 2nd arg, i.e. the inverse of sum.)
Enjoy, rwg
RWG@MIT-MC 04/21/77 12:06:54
The fcns NUSUM and UNSUM in
SHARE;NUSUM >
now know a little about sums and differences of finite products, e.g.
unsum(prod(i^2,i,1,n),n) ==> (n-1)*(n+1)*prod(i^2, i,1,n-1) and
nusum(%,n,1,n) ==> prod(i^2,i,1,n) - 1 .