θ函数的交替循环求和公式及其应用

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-06-26 DOI:10.2298/AADM120204004Z

Jun-Ming Zhu

引用次数: 7

摘要

我们证明了θ函数的一个通用的交替循环求和公式，它隐含了大量的θ函数恒等式。特别是，我们从这个身份中恢复了拉马努詹笔记本中的几个身份。我们还得到了（q；q）2n∞的两个公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

AN ALTERNATE CIRCULAR SUMMATION FORMULA OF THETA FUNCTIONS AND ITS APPLICATIONS

We prove a general alternate circular summation formula of theta functions, which implies a great deal of theta-function identities. In particular, we recover several identities in Ramanujan's Notebook from this identity. We also obtain two formulaes for (q; q)2n∞.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).