The q-analog of the factorial (by analogy with the q-gamma function).
For an integer, the -factorial is defined by
(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
See also
q-Beta Function,
q-Binomial Coefficient,
q-Bracket,
q-Cosine,
q-Gamma Function,
q-Pi,
q-Sine
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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.Referenced on
Wolfram|Alpha
q-Factorial
Cite this as:
Weisstein, Eric W. "q-Factorial." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/q-Factorial.html
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