Generalized Pochhammer symbol

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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.