A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY*

doi:10.1007/s10473-023-0608-3

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2449-2470.doi: 10.1007/s10473-023-0608-3

A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*

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

收稿日期:2022-06-06 修回日期:2023-05-29 发布日期:2023-12-08
作者简介:Zhiguo LIU, E-mail: zgliu@math.ecnu.edu.cn; liuzg@hotmail.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11971173) and the Science and Technology Commission of Shanghai Municipality (22DZ2229014).

A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*

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

Received:2022-06-06 Revised:2023-05-29 Published:2023-12-08
About author:Zhiguo LIU, E-mail: zgliu@math.ecnu.edu.cn; liuzg@hotmail.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11971173) and the Science and Technology Commission of Shanghai Municipality (22DZ2229014).

摘要/Abstract

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 $_6\psi_6$ 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 $_3\psi_3$ series is proved.

关键词: $q$ -hypergeometric series, $q$ -exponential differential operator, Bailey's $_6\psi_6$ summation, double $q$ -hypergeometric series, $q$ -partial differential equation

Abstract: 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 $_6\psi_6$ 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 $_3\psi_3$ series is proved.

Key words: $q$ -hypergeometric series, $q$ -exponential differential operator, Bailey's $_6\psi_6$ summation, double $q$ -hypergeometric series, $q$ -partial differential equation

中图分类号:

05A30

Zhiguo LIU. A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*[J]. 数学物理学报(英文版), 2023, 43(6): 2449-2470.

Zhiguo LIU. A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2449-2470.

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A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*

A MULTIPLE q-EXPONENTIAL DIFFERENTIAL OPERATIONAL IDENTITY^*

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