A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY  

作　　者：刘治国 Zhiguo LIU(School of Mathematical Sciences,Key Laboratory of MEA(Ministry of Education)&Shanghai Key Laboratory of PMMP,East China Normal University,Shanghai 200241,China)

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,China

出　　处：《Acta Mathematica Scientia》2023年第6期2449-2470,共22页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (11971173);the Science and Technology Commission of Shanghai Municipality (22DZ2229014).

摘　　要：Using Hartogs’fundamental theorem for analytic functions in several complex variables and q-partial differential equations,we establish a multiple q-exponential differential formula for analytic functions in several variables.With this identity,we give new proofs of a variety of important classical formulas including Bailey’s 6ψ6 series summation formula and the Atakishiyev integral.A new transformation formula for a double q-series with several interesting special cases is given.A new transformation formula for a 3ψ3 series is proved.

关 键 词：q-hypergeometric series q-exponential differential operator Bailey's 6b6 summation double q-hypergeometric series q-partial differential equation 

分 类 号：O175[理学—数学]