The Operator S(a,b;θ_x ) for the Polynomials Z_n (x,y,a,b;q)

Authors

  • Husam L. Saad Department of Mathematics, College of Science, Basrah University, Basrah, Iraq https://orcid.org/0000-0001-8923-4759
  • Faiz A. Reshem Department of Mathematics, College of Science, Basrah University, Basrah, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.10.26

Keywords:

The bivariate Rogers-Szegö polynomials, Generating function, Rogers formula, Inverse linearisation formula, q-difference equation

Abstract

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials .

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Published

2022-10-30

How to Cite

Saad, H. L., & Reshem, F. A. (2022). The Operator S(a,b;θ_x ) for the Polynomials Z_n (x,y,a,b;q). Iraqi Journal of Science, 63(10), 4397–4409. https://doi.org/10.24996/ijs.2022.63.10.26

Issue

Section

Mathematics