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

• Shahid Ahmad Wani ^[1] ; Subuhi Khan ^[1]
  1. [1] Aligarh Muslim University

     Aligarh Muslim University

     India

     
• Localización: Boletín de la Sociedad Matemática Mexicana: Tercera Serie, ISSN 1405-213X, ISSN-e 2296-4495, Vol. 26, Nº. 3, 2020, págs. 947-971
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.