Certain properties and applications of the 2D Sheffer and related polynomials

Abstract

In this article, the 2D Sheffer polynomials are introduced and their quasi-monomial properties are established. Further, certain properties of the 2D Sheffer polynomials are studied by making use of matrix algebra. This approach offers a powerful tool for investigating properties of the multi-variable special polynomials. The recursive formulae and differential equation for these polynomials are established using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the 2D associated Sheffer and 2D Appell families are also derived. Further, these results are demonstrated for the truncated exponential–Sheffer and Legendre–Sheffer families and also for certain members of these families.

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Correspondence to Shahid Ahmad Wani.

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Wani, S.A., Khan, S. Certain properties and applications of the 2D Sheffer and related polynomials. Bol. Soc. Mat. Mex. 26, 947–971 (2020). https://doi.org/10.1007/s40590-020-00280-5

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Keywords

  • 2D Sheffer polynomials
  • Monomiality principle
  • Pascal functional matrix
  • Wronskian matrix
  • Recursive formulae
  • Differential equation

Mathematics Subject Classification

  • 15A15
  • 15A24
  • 33E30
  • 65QXX