Generalized Pochhammer symbol

In mathematics, the generalized Pochhammer symbol of parameter $\alpha>0$ and partition $\kappa=(\kappa_1,\kappa_2,\ldots,\kappa_m)$ generalizes the classical Pochhammer symbol, named after Leo August Pochhammer, and is defined as

$(a)^{(\alpha )}_\kappa=\prod_{i=1}^m \prod_{j=1}^{\kappa_i} \left(a-\frac{i-1}{\alpha}+j-1\right).$

It is used in multivariate analysis.