多重q指数微分运算恒等式

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2023-11-06 DOI:10.1007/s10473-023-0608-3

Zhiguo Liu

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引用次数: 0

摘要

利用多复变量解析函数的Hartogs基本定理和q偏微分方程，建立了多复变量分析函数的多重q指数微分公式。利用这个恒等式，我们给出了许多重要经典公式的新证明，包括Bailey的6ψ6级数求和公式和Atakishiyev积分。给出了双q级数的一个新的变换公式，它有几个有趣的特例。证明了一个新的3ψ3级数的变换公式。

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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.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

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.