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-factorial

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.1)