<<RISC`qSimplify`

Package qSimplify version 1.1 written by Axel Riese
Copyright Research Institute for Symbolic Computation (RISC),
Johannes Kepler University, Linz, Austria

qSimplify[qFactorial[3,q]]

qSimplify[qFactorial[2,q]]

qSimplify[qFactorial[3,q]]

qSimplify[qPochhammer[x,q,0]]

qSimplify[qPochhammer[x,q,5]]

qSimplify[qBinomial[6,3,q]]

qSimplify[qBinomial[n,k,q]/qBinomial[n,k-1,q]]

qPowerExpand[(q^a)^b]

qPowerExpand[q^(Binomial[n,2]-Binomial[n-k,2])]

Table[Sum[q^(k^2)qBinomial[n,k,q],{k,0,n}]==Sum[(-1)^k q^(k(5k+1)/2)qBinomial[2n,n+2k,q],{k,-n,n}],{n,0,5}]//qSimplify//FullSimplify

Table[Sum[(-1)^k q^(k(2k-1)) qBinomial[2j,j+k,q^2],{k,-j,j}],{j,0,5}]//qSimplify//Factor