Integral representations for the Al-Salam-Carlitz polynomials and an extension of the q-Vandermonde summation - Wang, Xiang-Li; Liu, Dong-Fang; Luo, Qiu-Ming (Utilitas Mathematica, 2016)
In this paper, by applying the q-operator way, we obtain the q-integral representations for the generalized Al-Salam-Carlitz polynomials and extend the q-Vandermonde summation. We also give a simple proof for Heine's transformation formula.