q-Difference Equation for the Operator E ̃(x,a;θ) and their Applications for the Polynomials h_n (a,b,x|q^(-1))
q-difference equation
generating function
Rogers formula
Mehler’s formula
homogeneous q-shift operator
Srivastava-Agarwal type generating function
This paper concentrates on employing the -difference equations approach to prove another generating function, extended generating function, Rogers formula and Mehler’s formula for the polynomials , as well as thegenerating functions of Srivastava-Agarwal type. Furthermore, we establish links between the homogeneous -difference equations and transformation formulas.
