Q-exponential Operator And Its Applications

Operator method is one of the effective means to study the q-series problem.In this paper,q-exponential operator is used to study the q-series on the basis of the existing results.The main contents are as follows:1.Starting from the q-Chu-Vandermonde formula,this paper uses q-exponential operator to act on some rational functions,and then applies the related properties of qexponential operator to obtain the corresponding q-exponential operator identities,and gives the related recursion formulas.2.By applying q-exponential operator to q-binomial theorem and q-Chu-Vandermonde formula,some q-series identities are obtained,and an identity of the operator r?s is derived from the more general q-exponential operator r?s and q-Leibniz formula,which is a generalization of some known identities.