A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials

@article{Kim2001ACF,
  title={A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials},
  author={Dongsu Kim and Jiang Zeng},
  journal={Eur. J. Comb.},
  year={2001},
  volume={22},
  pages={313-332}
}
We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner?Pollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meixner?Pollaczek polynomials. Our proof is based on some explicit bijections and sign-reversing weight-preserving involutions. 
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