<<MultiSum.m

MultiSum Package by Kurt Wegschaider (enhanced by Axel Riese and Burkhard Zimmermann) — © RISC Linz — V 2.02β (02/21/05)

TermFactor=Binomial[i+j,i](-1)^k Pochhammer[-α-i-j,k]/Factorial[k]

NonStandardLaguerreterm=TermFactor Pochhammer[-k,r+s]Pochhammer[-β-i,r]Pochhammer[-i,r]Pochhammer[-γ-j,s]Pochhammer[-j,s]/(Factorial[r]Factorial[s]Pochhammer[-α-i-j,r+s] Pochhammer[-i-j,r+s])

Timing[rec=SumCertificate[FindCertificate[NonStandardLaguerreterm,k,{r,s},1]]]

res=Map[Factor,rec [[1,1]]/.{k->k+2,SUM->S}]