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