Difference between revisions of "Q-number"
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| − | Let $q \in \mathbb{C} \setminus \{1\}$ | + | Let $a \in \mathbb{C}$ and $q \in \mathbb{C} \setminus \{0,1\}$. Define the $q$-number $[a]_q$ by |
| − | + | $$[a]_q=\dfrac{1-q^a}{1-q}.$$ | |
| − | + | We define $[0]_q=0$ and if $a_n \in \left\{1,2,\ldots \right\}$, then we get | |
| − | $$[ | + | $$[n]_q = \displaystyle\sum_{k=1}^n q^{k-1}.$$ |
| + | |||
| + | =References= | ||
| + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=findme|next=}}: (6.1) | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Revision as of 22:24, 16 June 2016
Let $a \in \mathbb{C}$ and $q \in \mathbb{C} \setminus \{0,1\}$. Define the $q$-number $[a]_q$ by $$[a]_q=\dfrac{1-q^a}{1-q}.$$ We define $[0]_q=0$ and if $a_n \in \left\{1,2,\ldots \right\}$, then we get $$[n]_q = \displaystyle\sum_{k=1}^n q^{k-1}.$$
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous): (6.1)
