初等复变理论在广义sinc（p）及相关积分中的应用

Q2 Agricultural and Biological Sciences

Transactions of The Royal Society of South Africa Pub Date : 2022-01-02 DOI:10.1080/0035919X.2021.2005716

J. Hey

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引用次数: 0

摘要

复变量理论在早期论文中的初步应用[Hey，J.D.2020。关于初等复变理论在sinc及相关积分中的应用。南非皇家学会学报75（3）：295–306]通过使用下面定义的广义sinc（p）函数进行了扩展，以便对Borwein积分的行为提供一些有趣的、额外的见解，这是应用于柯西定理的Jordan引理的简单结果。本处理与分析实验室和天体物理等离子体中离子微扰器的电场引起的谱线加宽有关，具有物理意义。最后，一个结果，在著名的论文[Whittaker，E.T.&Watson，G.N.1927中被称为学生问题。《现代分析教程》，第六章（第四版），剑桥大学出版社]，是在sinc（p）函数的帮助下用更一般的术语表述的。数值表广泛地说明了本分析结果应用的简单性。

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On elementary complex variable theory applied to generalised sinc(p) and related integrals

The elementary application of complex variable theory in an earlier paper [Hey, J.D. 2020. On elementary complex variable theory applied to sinc and related integrals. Transactions of the Royal Society of South Africa 75(3): 295–306] is extended by use of the generalised sinc(p) function defined below, in order to provide some interesting, additional insight into the behaviour of the Borwein integrals, which arise as simple consequences of Jordan’s lemma applied to Cauchy’s theorem. The present treatment is of physical interest in relation to the analysis of spectral line broadening by the electric fields of ion perturbers in laboratory and astrophysical plasmas. Finally, a result, stated as a student problem in the well-known treatise [Whittaker, E.T. & Watson, G.N. 1927. A Course of Modern Analysis, Ch. VI (4th ed.). Cambridge University Press], is formulated in more general terms with the aid of the sinc(p) function. The simplicity of application of the present analytical results is extensively illustrated by numerical tables.

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来源期刊

Transactions of The Royal Society of South Africa Agricultural and Biological Sciences-Agricultural and Biological Sciences (all)

CiteScore

2.80

自引率

0.00%

发文量

期刊介绍： Transactions of the Royal Society of South Africa , published on behalf of the Royal Society of South Africa since 1908, comprises a rich archive of original scientific research in and beyond South Africa. Since 1878, when it was founded as Transactions of the South African Philosophical Society, the Journal’s strength has lain in its multi- and inter-disciplinary orientation, which is aimed at ‘promoting the improvement and diffusion of science in all its branches’ (original Charter). Today this includes natural, physical, medical, environmental and earth sciences as well as any other topic that may be of interest or importance to the people of Africa. Transactions publishes original research papers, review articles, special issues, feature articles, festschriften and book reviews. While coverage emphasizes southern Africa, submissions concerning the rest of the continent are encouraged.