The Operator S(a,b;θ_x ) for the Polynomials Z_n (x,y,a,b;q)
Keywords:The bivariate Rogers-Szegö polynomials, Generating function, Rogers formula, Inverse linearisation formula, q-difference equation
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 .