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Towards the Centenary of Sheffer Polynomial Sequences: Old and Recent Results

Author

Listed:
  • Francesco Aldo Costabile

    (Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy)

  • Maria Italia Gualtieri

    (Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy)

  • Anna Napoli

    (Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy)

Abstract

Sheffer’s work is about to turn 100 years after its publication. In reporting this important event, we recall some interesting old and recent results, aware of the incompleteness of the wide existing literature. Particularly, we recall Sheffer’s approach, the theory of Rota and his collaborators, the isomorphism between the group of Sheffer polynomial sequences and the so-called Riordan matrices group. This inspired the most recent approaches based on elementary matrix calculus. The interesting problem of orthogonality in the context of Sheffer sequences is also reported, recalling the results of Sheffer, Meixner, Shohat, and the very recent one of Galiffa et al., and of Costabile et al.

Suggested Citation

  • Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2022. "Towards the Centenary of Sheffer Polynomial Sequences: Old and Recent Results," Mathematics, MDPI, vol. 10(23), pages 1-28, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4435-:d:982993
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    References listed on IDEAS

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    1. Isabel Cação & Paolo E. Ricci, 2011. "Monomiality Principle and Eigenfunctions of Differential Operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-15, May.
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    Cited by:

    1. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2022. "Polynomial Sequences and Their Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

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