archive/share/trash/nusum.usg

   1 The small set of functions from
   2                 loadfile(nusum,?>,dsk,share)
   3 is, I believe, a decision procedure for indefinite (i.e. FINITE)
   4 hypergeometric summation.  Restrictions:
   5         1) Both the summand and the answer must be expressible as products
   6 of nth pwrs, factorials, binomials, and rational fcns.
   7
   8         Examples:
   9 nusum(n*n!,n,0,n);                      ==>  (n+1)! - 1
  10 nusum(n^4*4^n/binomial(2*n,n),n,0,n);   ==>  <moby mess>
  11 unsum(%,n);                             ==>  n^4*4^n/binomial(2*n,n)
  12         etc.
  13 (UNSUM was formerly called DELTA, and is just the first backward
  14 difference w.r.t. its 2nd arg, i.e. the inverse of sum.)
  15
  16 Enjoy,  rwg
  17
  18
  19 RWG@MIT-MC 04/21/77 12:06:54
  20
  21 The fcns NUSUM and UNSUM in
  22                 SHARE;NUSUM >
  23 now know a little about sums and differences of finite products, e.g.
  24 unsum(prod(i^2,i,1,n),n)        ==>  (n-1)*(n+1)*prod(i^2, i,1,n-1) and
  25 nusum(%,n,1,n)                  ==>  prod(i^2,i,1,n) - 1 .