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Date: 8-8-2019
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The q-analog of the factorial (by analogy with the q-gamma function). For an integer, the -factorial is defined by
(1) |
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(2) |
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(3) |
(Koepf 1998, p. 26). For ,
(4) |
where is the q-gamma function.
-factorials are implemented in the Wolfram Language as QFactorial[n, q].
The first few values are
(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
REFERENCES:
Gasper, G. and Rahman, M. Basic Hypergeometric Series. Cambridge, England: Cambridge University Press, 1990.
Gosper, R. W. "Experiments and Discoveries in q-Trigonometry." In Symbolic Computation, Number Theory,Special Functions, Physics and Combinatorics. Proceedings of the Conference Held at the University of Florida, Gainesville, FL, November 11-13, 1999 (Ed. F. G. Garvan and M. E. H. Ismail). Dordrecht, Netherlands: Kluwer, pp. 79-105, 2001.
Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, pp. 26 and 30, 1998.
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