Q-number

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

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

See Also

$q$-factorial

References

• D.S. McAnally: q-exponential and q-gamma functions. I. q-exponential functions (1994)... (previous)... (next) $(2.3)$
• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.1$) (calls $[a]_q$ $\{a\}_q$)