Abstract We derive the connection relations between three q-Taylor polynomial bases. We also derive the connection relations between two of these bases and the continuous q-Hermite polynomials, as well as several new generating functions for the continuous q-Hermite polynomials. Our results also lead to some new integral evaluations. Using one of these connection relations, we give a new proof of a general addition theorem of Suslov for the q-exponential function E q of Ismail and Zhang.

中文翻译：

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q-Taylor 多项式基的连接关系

摘要 我们推导出三个q-Taylor多项式基之间的联系关系。我们还推导出其中两个基与连续 q-Hermite 多项式之间的连接关系，以及连续 q-Hermite 多项式的几个新生成函数。我们的结果也导致了一些新的积分评估。使用这些连接关系中的一个，我们对 Ismail 和 Zhang 的 q 指数函数 E q 给出了 Suslov 的一般加法定理的新证明。