Some 𝑞-identities derived by the ordinary derivative operator

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/proc/16817

Jin Wang, Ruiqi Ruan

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引用次数: 0

Abstract

In this paper, we investigate applications of the ordinary derivative operator, instead of the q q -derivative operator, to the theory of q q -series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the q q -binomial theorem, Ramanujan’s 1 ψ 1 {}_1\psi _1 formula, the quintuple product identity, Gasper’s q q -Clausen product formula, and Rogers’ 6 ϕ 5 {}_6\phi _5 formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein’s theorem on Lambert series.

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由普通导数算子推导出的一些Δ常数

本文研究了普通导数算子而非 q q -导数算子在 q q -数列理论中的应用。作为主要成果，我们建立了许多新的求和与变换公式，它们与一些著名公式密切相关，如 q q -二项式定理、Ramanujan 的 1 ψ 1 {}_1\psi _1 公式、五次乘积同一性、Gasper 的 q q -Clausen 乘积公式和 Rogers 的 6 ϕ 5 {}_6\phi _5 公式等。在这些结果中，有罗杰斯-拉马努扬特性的有限形式，也有爱森斯坦兰伯特级数定理的捷径。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.