QDifferenceEquations[QPochhammer] - q-Pochhammer symbol
QDifferenceEquations[QBinomial] - q-binomial coefficient
QDifferenceEquations[QBrackets] - q-brackets
QDifferenceEquations[QFactorial] - q-factorial
QDifferenceEquations[QGAMMA] - q-Gamma
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Calling Sequence
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QPochhammer(a, q, infinity)
QPochhammer(a, q, k)
QBinomial(n, k, q)
QBrackets(k, q)
QFactorial(k, q)
QGAMMA(a, q)
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Parameters
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a
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algebraic expression
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q
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name used as the parameter q, or an integer power of a name
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k
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symbolic integer value
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n
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symbolic integer value
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Description
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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 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.
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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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Examples
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Compute the certificate of H (which is a rational function in ):
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References
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Boeing, H., and Koepf, W. "Algorithms for q-hypergeometric summation in computer algebra." Journal of Symbolic Computation. Vol. 11. (1999): 1-23.
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