Generalized Pochhammer symbol

In mathematics, the generalized Pochhammer symbol of parameter ${\displaystyle \alpha >0}$ and partition ${\displaystyle \kappa =(\kappa _{1},\kappa _{2},\ldots ,\kappa _{m})}$ generalizes the classical Pochhammer symbol, named after Leo August Pochhammer, and is defined as

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

It is used in multivariate analysis.