The QDifferenceEquations package supports five q-hypergeometric terms. They are q-Pochhammer symbol, q-binomial coefficient, q-brackets, q-factorial, and q-Gamma, which correspond to the five functions QPochhammer, QBinomial, QBrackets, QFactorial, and QGAMMA.

These functions are place holders for the q-objects. The command expand allows expansion of these objects. The command  allows the re-write of QBinomial, QBrackets, QFactorial, and QGAMMA in terms of QPochhammer symbols.

The five q-hypergeometric objects are defined as follows.

Note that  (the compact Gasper and Rahman notation) means .

The commands QSimpComb and QSimplify are for simplification of expressions involving these q-objects.

This implementation is mainly based on the implementation by H. Boeing, W. Koepf. See the References section.

Boeing, H., and Koepf, W. "Algorithms for q-hypergeometric summation in computer algebra." Journal of Symbolic Computation. Vol. 11. (1999): 1-23.