The function defined by
![[n]_q](/images/equations/q-Bracket/Inline1.svg) |  | ![[n; 1]_q](/images/equations/q-Bracket/Inline3.svg) |
(1)
|
 |  |  |
(2)
|
for integer 
,
where ![[n; k]_q](/images/equations/q-Bracket/Inline8.svg)
is a q-binomial
coefficient.
The 
-bracket satisfies
![lim_(q->1^-)[n]_q=n.](/images/equations/q-Bracket/NumberedEquation1.svg) |
(3)
|
q-Bracket
See also
q-Binomial Coefficient, q-FactorialExplore with Wolfram|Alpha
References
Gasper, G. and Rahman, M. Basic Hypergeometric Series. Cambridge, England: Cambridge University Press, 1990.Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 26, 1998.Referenced on Wolfram|Alpha
q-BracketCite this as:
Weisstein, Eric W. "q-Bracket." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/q-Bracket.html