Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications

In this paper, by the method of comparing coefficients, we establish a new generating function of multivariable Al-Salam-Carlitz polynomials which contains both Rogers’ and Bowman’s symmetirc expansion formulas and the classical $q$-Mehler formula as special cases. Some new $q$-series identities related to the multivariable Al-Salam-Carlitz polynomials are also presented.