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Article Navigation> JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY> 2015> 24(3): 298-304
LAO Da-zhong, ZHAO Shan-shan, LAO Tian-fu. Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam, Bernoulli numbers and Euler numbers[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2015, 24(3): 298-304. doi: 10.15918/j.jbit1004-0579.201524.0303
Citation: LAO Da-zhong, ZHAO Shan-shan, LAO Tian-fu. Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam, Bernoulli numbers and Euler numbers[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2015, 24(3): 298-304.doi:10.15918/j.jbit1004-0579.201524.0303
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Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam, Bernoulli numbers and Euler numbers

doi:10.15918/j.jbit1004-0579.201524.0303
  • 1.

    School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

  • 2.

    Dandong Design Institute of Chemical Fibre, Dandong, Liaoning 118002, China

  • 3.

    China National General Machinery Engineering Corporation, Beijing 100050, China

  • Received Date:2014-01-08
    Abstract
  • 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.
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    • References (10)
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