Abstract
The formula for \(\pi \) as an infinite product known as the Wallis formula was developed by John Wallis in 1655 by methods that pre-date the establishment of calculus. Herein I introduce said formula with its original derivation. Then I show how, 360 years later, Carl Hagen and I rediscovered this 17th century formula in the quantum mechanics of the hydrogen atom.
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For example, the ratio is .849, .906, .932, .978, .988 for \(\ell = 0,1,2, 10, 20\).
References
L. Berggren, J. Borwein, and P. Borwein, Pi: A source book, Springer-Verlag (1997).
T. Friedmann, C.R. Hagen, J. Math. Phys. 56 (2015) 112101.
V.J. Katz, A History of Mathematics: an Introduction, Addison-Wesley (2009).
J.A. Stedall, Arch. Hist. Exact Sci. 56 (2001) 1–28.
J. Wallis, Arithmetica Infinitorum, Oxford, 1655.
Acknowledgements
The author is grateful to Vladimir Dobrev for the invitation to give this plenary talk and for organizing this excellent conference.
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Friedmann, T. (2018). On the Derivation of the Wallis Formula for \(\pi \) in the 17th and 21st Centuries. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_4
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DOI: https://doi.org/10.1007/978-981-13-2715-5_4
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