A Multiple q-translation Formula and Its Implications  

作　　者：Zhi Guo LIU 

机构地区：[1]School of Mathematical Sciences,Key Laboratory of MEA(Ministry of Education)&Shanghai Key Laboratory of PMMP,East China Normal University,Shanghai 200241,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第12期2338-2363,共26页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11971173);Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。

摘　　要：Using Hartogs'fundamental theorem for analytic functions in several complex variables,we establish a multiple q-exponential differential operational identity for the analytic functions in several variables,which can be regarded as a multiple q-translation formula.This multiple q-translation formula is a fundamental result and play a pivotal role in q-mathematics.Using this q-translation formula,we can easily recover many classical conclusions in q-mathematics and derive some new q-formulas.Our work reveals some profound connections between the theory of complex functions in several variables and q-mathematics.

关 键 词：Q-SERIES q-beta integral q-exponential differential operator q-translation Rogers-Szego polynomials 

分 类 号：O172[理学—数学]