The rectangular elastic membrane for Apery’s and Catalan’s constants calculation

Franck Delplace

Abstract


In this paper, we use the elastic membrane model to calculate Apéry’s constant and others associated series. The de Saint-Venant’s solution of Poisson’s partial differential equation with rectangular boundary is used for the two limit cases of thin and square membranes. Gradient calculations at the boundaries give a relationship involving ratio 𝜋 𝐺⁄𝜁(3) where 𝐺 is the Catalan’s constant and a rapidly convergent series for 𝜁(3) analogous to famous Ramanujan’s series.

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How to Cite this Article:

Franck Delplace, The rectangular elastic membrane for Apery’s and Catalan’s constants calculation, Journal of Mathematical and Computational Science, Vol 9, No 5 (2019), 590-604

Copyright © 2019 Franck Delplace. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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