Viewing from polynomials solutions of q-difference equations makes certain generating functions calculated easily. In this short paper, we build the relations between Cigler’s polynomials and q-difference equations. In addition, we deduce generating functions and bilinear generating functions for Cigler’s polynomials. More over, we gain multilinear and mixed generating functions for Cigler’s polynomials. At last, we gain $U(n+1)$ type generating functions for Cigler’s polynomials.

Institute of Mathematics of the Czech Academy of Sciences