Generalized Pochhammer symbol

In mathematics, the generalized Pochhammer symbol of parameter $\alpha >0$ and partition $\kappa =({\kappa }_1,{\kappa }_2,\dots ,{\kappa }_m)$ generalizes the classical Pochhammer symbol, named after Leo August Pochhammer, and is defined as

$(a{)}_{\kappa }^{(\alpha )}=\prod _{i=1}^m\prod _{j=1}^{{\kappa }_i}(a-\frac{i-1}{\alpha }+j-1).$

It is used in multivariate analysis.