{"title":"多重q指数微分运算恒等式","authors":"Zhiguo Liu","doi":"10.1007/s10473-023-0608-3","DOIUrl":null,"url":null,"abstract":"<div><p>Using Hartogs’ fundamental theorem for analytic functions in several complex variables and <i>q</i>-partial differential equations, we establish a multiple <i>q</i>-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 <sub>6</sub><i>ψ</i><sub>6</sub> series summation formula and the Atakishiyev integral. A new transformation formula for a double <i>q</i>-series with several interesting special cases is given. A new transformation formula for a <sub>3</sub><i>ψ</i><sub>3</sub> series is proved.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2449 - 2470"},"PeriodicalIF":1.2000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A multiple q-exponential differential operational identity\",\"authors\":\"Zhiguo Liu\",\"doi\":\"10.1007/s10473-023-0608-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Using Hartogs’ fundamental theorem for analytic functions in several complex variables and <i>q</i>-partial differential equations, we establish a multiple <i>q</i>-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 <sub>6</sub><i>ψ</i><sub>6</sub> series summation formula and the Atakishiyev integral. A new transformation formula for a double <i>q</i>-series with several interesting special cases is given. A new transformation formula for a <sub>3</sub><i>ψ</i><sub>3</sub> series is proved.</p></div>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"43 6\",\"pages\":\"2449 - 2470\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10473-023-0608-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s10473-023-0608-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A multiple q-exponential differential operational identity
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.
期刊介绍:
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.