Difference between revisions of "Q-number"

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=References=
 
=References=
 
* {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=Q-derivative power rule|next=findme}} $(2.3)$ (calls $[a]_q$ $(a)_q$)
 
* {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=Q-derivative power rule|next=findme}} $(2.3)$ (calls $[a]_q$ $(a)_q$)
 +
* {{BookReference|Special Functions|1999|George E. Andrews|author2=Richard Askey|author3=Ranjan Roy|prev=findme|next=q-factorial}}
 
* {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=findme|next=q-number when a=n is a natural number}}: ($6.1$) (calls $[a]_q$ $\{a\}_q$)
 
* {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=findme|next=q-number when a=n is a natural number}}: ($6.1$) (calls $[a]_q$ $\{a\}_q$)
  
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 20:53, 18 December 2016

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

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

Notes

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

References