Difference between revisions of "Q-Binomial coefficient"

From specialfunctionswiki
Jump to: navigation, search
(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...")
 
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
The $q$-Binomial coefficient is
+
The $q$-Binomial coefficient ${n \brack k}_q$ is
$$\left[ \begin{array}{ll} n \\ k \end{array} \right]_q = \dfrac{(q;q)_n}{(q;q)_k(q;q)_{n-k}},$$
+
$${n \brack k}_q = \dfrac{(q;q)_n}{(q;q)_k(q;q)_{n-k}},$$
 
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

References