A method of deriving the Wallis formula and of decomposition of hyperbolic functions into infinite products
Matematičeskoe obrazovanie, no. 2 (2018), pp. 40-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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A simple method of decomposition of the hyperbolic tangent function into infinite product by the potential theory approach is suggested. This implies the famous Wallis formula.
Keywords: Hyperbolic tangent
Mots-clés : Wallis formula.
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S. N. Sazonov. A method of deriving the Wallis formula and of decomposition of hyperbolic functions into infinite products. Matematičeskoe obrazovanie, no. 2 (2018), pp. 40-43. http://geodesic.mathdoc.fr/item/MO_2018_2_a3/

[1] A.P. Yushkevich (red.), Istoriya matematiki s drevneishikh vremën do nachala XIX stoletiya, v. I–III, Nauka, M., 1970

[2] Whiteside D.T., “Patterns of Matematical Thought in the later Seventeenth Centur”, Arch. Hist. Exact Sci., I:4 (1961), 179–388 | DOI | MR | Zbl

[3] Smirnov V.I., Kurs vysshei matematiki, chast 2, gl. III, v. III, BKhV Peterburg, SPb:, 2010, 816 pp. | MR

[4] Friedmann T., Hagen C.R., “Quantum Mechanical Derivation of the Wallis Formula for $\pi $”, J. Math. Phys, 56:11 (2015), 112101 | DOI | MR | Zbl

[5] Tamm I.E., Osnovy teorii elektrichestva, glava 1, Nauka, M., 1976

[6] Landau L.D., Lifshits E.M., Elektrodinamika sploshnykh sred, §44, Nauka, M., 1983, 616 pp.