Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam, Bernoulli numbers and Euler numbers

被引：0
作者：
Lao, Da-Zhong [1 ]
Zhao, Shan-Shan [2 ]
Lao, Tian-Fu [3 ]
机构：
[1] School of Aerospace Engineering, Beijing Institute of Technology, Beijing
[2] Dandong Design Institute of Chemical Fibre, Dandong, 118002, Liaoning
[3] China National General Machinery Engineering Corporation, Beijing
来源：
Journal of Beijing Institute of Technology (English Edition) | 2015年 / 24卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Bernoulli numbers; Coefficients of beam; Equation of deflection curve; Euler numbers; Fourier series; Simple beam;
D O I：
10.15918/j.jbit1004-0579.201524.0303
中图分类号：
学科分类号：
摘要：
Based on the differential equation of the deflection curve for the beam, the equation of the deflection curve for the simple beam is obtained by integral. The equation of the deflection curve for the simple beam carrying the linear load is generalized, and then it is expanded into the corresponding Fourier series. With the obtained summation results of the infinite series, it is found that they are related to Bernoulli numbers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam, Bernoulli numbers and Euler numbers are found, and the relative mathematical formulas are presented. © 2015, Editorial Department of Journal of Beijing Institute of Technology. All right reserved.
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页码：298 / 304
页数：6
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