Difference between revisions of "Q-number"
From specialfunctionswiki
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=Properties= | =Properties= | ||
| − | [[q-number when a=n is a natural number]]<br /> | + | [[q-number when a=n is a natural number|$q$-number when $a=n$ is a natural number]]<br /> |
| − | [[q-factorial]]<br /> | + | [[q-number of a negative|$q$-number of a negative]]<br /> |
| + | [[1/q-number as a q-number]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[q-factorial|$q$-factorial]]<br /> | ||
Revision as of 08:00, 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
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.1$)
