Generalized Pochhammer symbol explained

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} ^{m} ^{i =1} \prod ^{\kappa _{i}} _{j =1} \left(a - (i -1)/(\alpha) + j -1 \right). It is used in multivariate analysis