Generalized Pochhammer symbol

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

( a ) κ ( α ) = ∏ i = 1 m ∏ j = 1 κ i ( a − i − 1 α + j − 1 ) . {\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.

References

  • Dunkl, Charles F.; Xu, Yuan (2001), Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and its Applications, vol. 81, Cambridge University Press, p. 308, ISBN 9780521800433
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