Some Characterization Problems Related to Sheffer Polynomial Sets

  • Hamza ChaggaraEmail author
  • Radhouan Mbarki
  • Salma Boussorra
Conference paper
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


In this work, we show some properties of Sheffer polynomials arising from quasi-monomiality. We survey characterization problems dealing with d-orthogonal polynomial sets of Sheffer type. We revisit some families in the literature and we state an explicit formula giving the exact number of Sheffer type d-orthogonal sets. We investigate, in detail, the (d + 1)-fold symmetric case as well as the particular cases d = 1, 2, 3.


Sheffer polynomials d-orthogonal polynomials Generating functions (d + 1)-fold symmetric polynomials Quasi-monomiality 

Mathematics Subject Classification (2000)

33C45 44A20 65D20 41A58 



We are much indebted to the organisers, Wolfram Koepf and Mama Foupouagnigni, of the AIMS-Volkswagen Stiftung Workshop on Introduction to Orthogonal Polynomials and Applications, Douala, Cameroon, October 5–12, 2018 for the invitation, the interesting program and the kind hospitality.

The first author would like to extend his appreciation to the Deanship of Scientific Research at King Khalid University for funding his work through research groups program under grant (2019).


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hamza Chaggara
    • 1
    • 2
    Email author
  • Radhouan Mbarki
    • 3
  • Salma Boussorra
    • 2
  1. 1.King Khalid University College of SciencesDepartment of MathematicsAbhaKingdom of Saudi Arabia
  2. 2.École Supérieure des Sciences et de la TechnologieUniversité de SousseSousseTunisia
  3. 3.Institut Préparatoire aux Études d’Ingénieur de MonastirUniversité de MonastirMonastirTunisia

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