A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect

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A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect

机译：基于傅里叶定期分布的求和方法和Casimir效应中产生的示例

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摘要

A generalised summation method is considered based on the Fourier series of periodic distributions. It is shown that

机译：基于傅里叶系列周期性分布来考虑广义求和方法。表明了这一点

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《Indagationes Mathematicae》 |2020年第3期|共28页
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正文语种 eng
中图分类数学;
关键词
Summation method; Ramanujan summation; Periodic distributions; Fourier series; Casimir effect;

机译：求和方法;ramanujan求和;周期性分布;傅立叶系列;卡西米尔效应;

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专利

1. A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect [J] . Indagationes Mathematicae . 2020,第3期

机译：基于傅里叶定期分布的求和方法和Casimir效应中产生的示例
2. Summation of Fourier Trigonometric Series and Conjugate Series by (C,α,β) Method [J] . L. N. Galoyan Journal of Contemporary Mathematical Analysis . 2011,第5期

机译：（C，α，β）方法对傅立叶三角级数和共轭级数求和
3. SUMMATION METHODS FOR FOURIER SERIES WITH RESPECT TO THE AZOFF-SHEHADA SYSTEM [J] . A. Pyshkin Journal of Mathematical Sciences . 2016,第5期

机译：相对于AZOFF-SHEHADA系统的Fourier级数的求和方法
4. Fourier Series Methods for Optimal Periodic Position Control [C] . Chayopitak, N., Taylor, . 2006

机译：最优周期位置控制的傅里叶级数方法
5. A large element computation for polygonal plates, shallow shells and cylindrical shells with the Fourier series and state-variable methods. [D] . Fu, Yee-Chung. 1996

机译：使用傅里叶级数和状态变量方法对多边形板，浅壳和圆柱壳进行大元素计算。
6. On the Application of Borels Method to the Summation of Fouriers Series [O] . Charles N. Moore 1925

机译：博耶方法在傅里叶级数求和中的应用
7. REGULAR SEMI-CONTINUOUS METHODS OF SUMMATION OF FOURIER SERIES [O] . A. D. Nakhman, B. P. Osilenker 2017

机译：傅立叶系列的定期半连续求和
8. Equivalence Between the Methods Involving Fourier Series and the Poisson's Summation Formula and Evaluation of a Class of Lattice Sums in Arbitrary Dimensions [R] . Dias, M., Chaba, A. N. 1985

机译：含傅里叶级数的方法与泊松Σ求和公式的等价性及任意维一类格的求和

A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect

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