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 authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng...The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.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
In this paper, the following are introduced briefly： the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non- commutative Weyl alge...In this paper, the following are introduced briefly： the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non- commutative Weyl algebra. We give an algorithm for proving the single-variable q-proper-hypergeometric identities that is based on Zeilberger＇s approach and the elimination in Weyl algebra. Finally, we test several examples that have been proven by D. Zeilberger and H. Will using the WZ-pair method and Gosper algorithm.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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501552,11871067supported by the National Natural Science Foundation of China under Grant No.11771433the Fund of the Youth Innovation Promotion Association,CAS
文摘The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.
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.
文摘In this paper, the following are introduced briefly： the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non- commutative Weyl algebra. We give an algorithm for proving the single-variable q-proper-hypergeometric identities that is based on Zeilberger＇s approach and the elimination in Weyl algebra. Finally, we test several examples that have been proven by D. Zeilberger and H. Will using the WZ-pair method and Gosper algorithm.
