Q-number

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Let $a \in \mathbb{C}$ and $q \in \mathbb{C} \setminus \{0,1\}$. Define the $q$-number $[a]_q$ by $$[a]_q=\dfrac{1-q^a}{1-q}.$$

Properties[edit]

$q$-number when $a=n$ is a natural number
$q$-number of a negative
1/q-number as a q-number

See Also[edit]

$q$-factorial

Notes[edit]

Mathworld calls $[a]_q$ the $q$-bracket

References[edit]