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 ...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.展开更多
The present paper is concerned with Bailey lemma which has been proved to be useful in the studies of hypergeometric function and Ramannujan-Rogers identities, etc. We will show that the Bailey lemma in ordinary form ...The present paper is concerned with Bailey lemma which has been proved to be useful in the studies of hypergeometric function and Ramannujan-Rogers identities, etc. We will show that the Bailey lemma in ordinary form is in fact a Riordan chain of a particular Riordan group.展开更多
基金supported by the National Natural Science Foundation of China (11971173)the Science and Technology Commission of Shanghai Municipality (22DZ2229014).
文摘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.
文摘The present paper is concerned with Bailey lemma which has been proved to be useful in the studies of hypergeometric function and Ramannujan-Rogers identities, etc. We will show that the Bailey lemma in ordinary form is in fact a Riordan chain of a particular Riordan group.
