/home/m262f99/RISC/MultiSum/demo1.nb

Math 262a, Fall 1999, Glenn Tesler
Demo of Kurt Wegschaider's MultiSum
10/27/99

<< MultiSum.m

?FindRecurrence

?SumCertificate

?CheckRecurrence

TraditionalForm[
      Sum[Binomial[n, j] Binomial[j, i] x^
            i y^(j - i) z^(n - j),   {i}, {j}]]

FindRecurrence[ 
      Binomial[n, j] Binomial[j, i] x^i y^(j - i) z^(n - j),  
      n,  {i, j}]

SumCertificate[%]

CheckRecurrence[%, (x + y + z)^n]

F1  =  
      Binomial[n, k] * Binomial[n + k, k] * 
        Binomial[k, j]^3

F2  =  Binomial[n, k] * Binomial[n + k, k]^2

FindRecurrence[F1, n, {j, k}]

SumCertificate[%]

Collect[%43[[1, 1]], 
      Table[SUM[n + kk], {kk, -10, 10}]]

FindRecurrence[F2, n, {k}]

SumCertificate[%]