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106.43 Another proof of ex/y being irrational

Published online by Cambridge University Press:  12 October 2022

Sourangshu Ghosh
Sourangshu Ghosh*
Affiliation:
Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India e-mail: [email protected]
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The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 523 - 525
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© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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References

Janot de Stainville, Mélanges d’analyse algébrique et de géométrie [A mixture of algebraic analysis and geometry], Veuve Courcier (1815) pp. 340-341.Google Scholar
Euler, Leonhard, De fractionibus continuis dissertatio [A dissertation on continued fractions] (PDF), Commentarii academiae scientiarum Petropolitanae 9 (1744) pp. 98-137.Google Scholar
Euler, Leonhard, An essay on continued fractions, Mathematical Systems Theory 18 (1985) pp. 295–398.Google Scholar
Edward Sandifer, C., How Euler did it, Mathematical Association of America (2007).Google Scholar
Cohn, Henry, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly, 113 (1) (2006) pp. 57–62.Google Scholar
MacDivitt, A. R. G., Yanagisawa, Yukio, An elementary proof that is irrational, Math. Gaz. 71 (October 1987) p. 217. e Google Scholar
Penesi, L. L., Elementary proof that is irrational, Amer. Math. Monthly 60 (7) (1953) p. 474. e Google Scholar
Apostol, T., Mathematical analysis (2nd edn.), Addison-Wesley (1974).Google Scholar
Liouville, Joseph, Sur l’irrationalité du nombre e = 2,718…. Journal de Mathématiques Pures et Appliquées. 1 (in French) 5 (1840) p. 192. Google Scholar
Hurwitz, Adolf, [1891]. Über die Kettenbruchentwicklung der Zahl e. Mathematische Werke (in German). 2. Birkhäuser (1933) pp. 129-133.Google Scholar
Liouville, Joseph, Addition à la note sur l’irrationalité du nombre, Journal de Mathématiques Pures et Appliquées. 1 (in French). 5 (1840) pp. 193-194.Google Scholar
Niven, Ivan, Irrational Numbers (1st edn.), 11 Mathematical Association of America, 1985.Google Scholar
Martin Aigner, Günter M. Ziegler, Proofs from THE BOOK (4th edn.), Springer-Verlag (1998) pp. 27–36.CrossRefGoogle Scholar
Nathan, J., The irrationality of for nonzero rational, Amer. Math. Monthly 105(8), (1998) pp. 762–763. ex x Google Scholar
Chrystal, G., Algebra: an elementary text-book for the higher classes of secondary schools and for colleges, Vol.II (1889).Google Scholar
Wall, H. S., Analytic Theory of Continued Fractions, Chelsea, New York (1948) pp. 335–361.Google Scholar
Borwein, J., Bailey, D. and Girgensohn, R., Experimentation in mathematics: computational paths to discovery, A K Peters, (2004) pp. 31–34.Google Scholar