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

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 $$[a]_q=\dfrac{1-q^a}{1-q}.$$

References