The Legendre-Stirling numbers

  title={The Legendre-Stirling numbers},
  author={George E. Andrews and Wolfgang Gawronski and Lance L. Littlejohn},
  journal={Discrete Mathematics},
The Legendre-Stirling numbers are the coeffi cients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejohn gave a combinatorial interpretation of the Legendre-Stirling numbers. In this paper, we establish… CONTINUE READING

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