Summation and Products

 

In Axiom

For comparison with other CAS choose from: Derive Macsyma Maple Mathematica Reduce

inputs outputs

    sum(n**2*x**n, n)

       2           3        2           2    2   n - 1
    ((n  - 2n + 1)x  + (- 2n  + 2n + 1)x  + n x)x
    --------------------------------------------------
                     3     2
                    x  - 3x  + 3x - 1
                                                     Type: Expression Integer

    sum(cos((2*r-1)*%pi/(2*n+1)), r)

     r
    --+      (2%A - 1)%pi
    >    cos(------------)
    --+         2n + 1
    %A
                                                     Type: Expression Integer

    product(%e**(sin(n*x)), n)

      n
    ++-++    sin(%A x)
     | |   %e
     | |
     %A
                                                     Type: Expression Integer

    for all n,m such that fixp m let
            factorial(n+m)=if m > 0 then factorial(n+m-1)*(n+m)
                       else factorial(n+m+1)/(n+m+1);

    sum(n*2**n/factorial(n+2), n)

     n        %A
    --+   %A 2
    >    ---------
    --+  (%A + 2)!
    %A
                                                     Type: Expression Integer