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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.
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These functions are placeholders 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.
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The five q-hypergeometric objects are defined as follows.
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Note that (the compact Gasper and Rahman notation) means .
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The commands QSimpComb and QSimplify are for simplification of expressions involving these q-objects.
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This implementation is mainly based on the implementation by H. Boeing, W. Koepf. See the References section.
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