Lao, Dazhong; Zhao, Shanshan; Lao, Tianfu Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam, Bernoulli numbers and Euler numbers. (English) Zbl 1349.11044 J. Beijing Inst. Technol. 24, No. 3, 298-304 (2015). Summary: 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 \(\pi\). 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. MSC: 11B68 Bernoulli and Euler numbers and polynomials 40A25 Approximation to limiting values (summation of series, etc.) 74K10 Rods (beams, columns, shafts, arches, rings, etc.) Keywords:Bernoulli numbers; Euler numbers; coefficients of beam; simple beam; equation of deflection curve; Fourier series PDFBibTeX XMLCite \textit{D. Lao} et al., J. Beijing Inst. Technol. 24, No. 3, 298--304 (2015; Zbl 1349.11044) Full Text: DOI