Difference between revisions of "Q-Binomial coefficient"
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(Created page with "The $q$-Binomial coefficient is $$\left[ \begin{array}{ll} n \\ k \end{array} \right]_q = \dfrac{(q;q)_n}{(q;q)_k(q;q)_{n-k}},$$ where $(q;q)_{\xi}$ denotes the q-Pochhammer...") |
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| − | The $q$-Binomial coefficient is | + | The $q$-Binomial coefficient ${n \brack k}_q$ is |
| − | $$ | + | $${n \brack k}_q = \dfrac{(q;q)_n}{(q;q)_k(q;q)_{n-k}},$$ |
where $(q;q)_{\xi}$ denotes the [[q-Pochhammer symbol]]. | where $(q;q)_{\xi}$ denotes the [[q-Pochhammer symbol]]. | ||
| + | |||
| + | =Properties= | ||
| + | [[q-Pochhammer as sum of q-binomial coefficients]] <br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 19:44, 15 December 2016
The $q$-Binomial coefficient ${n \brack k}_q$ is $${n \brack k}_q = \dfrac{(q;q)_n}{(q;q)_k(q;q)_{n-k}},$$ where $(q;q)_{\xi}$ denotes the q-Pochhammer symbol.
Properties
q-Pochhammer as sum of q-binomial coefficients
