三种q-算子的推广  

Generalizations of Three q -Operators

作　　者：黄代萍 HUANG Daiping(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《湖北民族大学学报（自然科学版）》2021年第1期62-66,共5页Journal of Hubei Minzu University:Natural Science Edition

基　　金：重庆市自然科学基金项目(cstc2019jcyj-msxmX0143).

摘　　要：为进一步研究算子方法在q-级数中的应用,首先引入了Cauchy算子、双参数有限q-指数算子以及三参数广义q-指数算子;然后在q-Chu-Vandermonde公式的基础上,应用这三个算子及其相关性质,推导出了几个新的q-算子恒等式,即Cauchy算子、双参数有限q-指数算子以及三参数广义q-指数算子这三者的推广.本文应用推广后的q-算子得到了关于q-二项式定理的一些推广,在之后的研究中也可用这几个推广形式来推导其它新的恒等式.In order to further study the applications of operator method in q-series,this paper first introduces the Cauchy operator,the finite q-exponential operator with two parameters and the generalized q-exponential operator with three parameters.Then,based on the q-Chu-Vandermonde formula,several new q-operator identities are derived by using these three operators and their related properties.Namely,they are the generalizations of the Cauchy operator,the finite q-exponential operator with two parameters and the generalized q-exponential operator with three parameters.In this paper,some generalizations about the q-binomial theorem are obtained by using the generalized q-operators,and other new identities can be derived by these generalizations in later studies.

关 键 词：Q-级数 Cauchy算子 双参数有限q-指数算子 三参数广义q-指数算子 q-Chu-Vandermonde公式 q-二项式定理 

分 类 号：O175.3[理学—数学]