两圆柱静电问题的四个解，以及由它们的等价性所产生的恒等式

IF 0.8 4区工程技术 Q3 MATHEMATICS, APPLIED Quarterly Journal of Mechanics and Applied Mathematics Pub Date : 2020-08-01 DOI:10.1093/qjmam/hbaa010

J. Lekner

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引用次数: 1

摘要

对于两个相等的圆形平行导电圆柱体周围的电势分布，存在四种不同的解决方案，充电到相同的电势。证明了它们的等价性，并讨论了由此产生的分析恒等式。这些恒等式涉及Jacobi椭圆函数$sn$、Jacobiθ函数$\theta_1、~\theta_2$以及三角函数和双曲函数上的无穷级数。

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Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence

Four distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic functions.

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来源期刊

Quarterly Journal of Mechanics and Applied Mathematics 物理-力学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly Journal of Mechanics and Applied Mathematics publishes original research articles on the application of mathematics to the field of mechanics interpreted in its widest sense. In addition to traditional areas, such as fluid and solid mechanics, the editors welcome submissions relating to any modern and emerging areas of applied mathematics.