Difference between revisions of "Second q-shifted factorial"
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\displaystyle\prod_{k=0}^{n-1} (1-q^{a+m}), & n=1,2,\ldots | \displaystyle\prod_{k=0}^{n-1} (1-q^{a+m}), & n=1,2,\ldots | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | If $(a)=(a_1,a_2,\ldots,a_m)$ is a vector then we define the notation | ||
| + | $$\langle (a);q \rangle_n = \langle a_1,a_2,\ldots,a_m; q \rangle_n = \displaystyle\prod_{j=1}^m \langle a_j;q \rangle_n.$$ | ||
Revision as of 20:17, 3 June 2016
The $q$-shifted factorial $\langle a;q \rangle_n$ is given by $$\langle a;q \rangle_n = \left\{ \begin{array}{ll} 1, & n=0; \\ \displaystyle\prod_{k=0}^{n-1} (1-q^{a+m}), & n=1,2,\ldots \end{array} \right.$$ If $(a)=(a_1,a_2,\ldots,a_m)$ is a vector then we define the notation $$\langle (a);q \rangle_n = \langle a_1,a_2,\ldots,a_m; q \rangle_n = \displaystyle\prod_{j=1}^m \langle a_j;q \rangle_n.$$
