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Euler's limit for ex and the exponential series

Published online by Cambridge University Press:  31 October 2008

A. J. Macintyre
Affiliation:
The University, Aberdeen
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1948 is the bicentenary of Euler's discovery that

This note gives a brief account of the subsequent work on these relations and a proof of the equivalence of limit and series which appears to involve new features.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1949

References

REFERENCES

1. Bromwich, T. J. I'a.. An introduction to the theory of infinite series, (1926) 170172 and 440441.Google Scholar
2. Cauchy, A. L.. Cours d'analyse de l'école polytechnique, 1re Partie. Analyse algébrique, Paris (1821).Google Scholar
3. Cauchy, A. L.. Résumé des léçons sur le calcul infinitésimal, Paris (1823).Google Scholar
4. Cauchy, A. L.. Léçons sur le calcul différentiel, Paris (1829). (See Œuvres Complètes, IIe série, III 147–149, IV 14–16, 224, 280–281, 385–6.Google Scholar
5. Chrystal, G.. Algebra, 37 (1889) 7779.Google Scholar
6. Durell, C. V.. Advanced Algebra, 37 (1932) 128.Google Scholar
7. Euler, L.. Introductio in analysin infinitorum, 37, Lausanne (1748) 8691.Google Scholar
8. Ferrar, W. L.. A textbook of convergence, (1938) 135–7.Google Scholar
9. Fort, O.. Ueber ein paar Ungleichungen und Grenzwerthe, Zeitschr. für Math. und Phys. 37 (1862) 4649.Google Scholar
10. Gibson, G. A.. An elementary treatise on the calculus, (1924) 9296.Google Scholar
11. Hardy, G. H.. Pure Mathematics, (1933) 137, 368–9, 379.Google Scholar
12. Hobson, E. W.. Plane Trigonometry, (1897) 274–5.Google Scholar
13. Hobson, E. W.. The theory of functions of a real variable, 37 (1926) 122.Google Scholar
14. Hyslop, J. M.. Infinite Series, (1942) 21.Google Scholar
15. Knopp, K.. Theorie und Anwendung der unendlichen Reihen, (1931) 196–7, 8384. English trans. (1928) 193–4, 80–81.Google Scholar
16. Levi, B.. Sopra l'integrazione delle serie. Lomb. Inst. Rend. (2) 37 (1906) 775780.Google Scholar
17. Littlewood, J. E.. Lectures on the theory of functions, (1944) 9293.Google Scholar
18. Milne, W. P.. Higher Algebra, (1921) 267–8.Google Scholar
19. Phillips, E. G.. A Course of Analysis, (1930) 4950.Google Scholar
20. Stewart, C. A.. Advanced Calculus, (1940) 9899.Google Scholar
21. Schlömilch, O., R. Courant Zeitschr. für Math, und Phys., 37 (1858) 387.Google Scholar
22. Tannery, J.. Introduction à la théorie des Fonctions d'une Variable, 37 (1904) 292, 301–3.Google Scholar