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Intriguing integrals: an Euler-inspired odyssey

Published online by Cambridge University Press:  01 August 2016

Nick Lord
Nick Lord*
Affiliation:
Tonbridge School, Kent TN9 1JP
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Type
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Information
The Mathematical Gazette , Volume 91 , Issue 522 , November 2007 , pp. 415 - 427
Copyright
Copyright © The Mathematical Association 2007

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References

1. Davis, P. J. Leonhard Euler’s integral: a historical profile of the gamma function, Amer. Math. Monthly 66 (1959) pp. 849–869.Google Scholar
2. Chapman, Robin Evaluating ζ (2), http://secamlocal.ex.ac.uk/∼rjc/etc/zeta2.pdf.Google Scholar
3. Sandifer, Ed How Euler did it: Basel problem with integrals (March 2004) http://www.maa.org/news/howeulerdidit.html Google Scholar
4. Ayoub, R. Euler and the zeta function, Amer. Math. Monthly 81 (1974) pp. 1067–1086.Google Scholar
5. Spivak, M. Calculus, Addison-Wesley (1967) p. 325.Google Scholar
6. Adamchik, V. 33 representations for Catalan’s constant, http://www.cs.cmu.edu/∼adamchik/articles/catalan/catalan.htmGoogle Scholar
7. Weil, A. Number theory: an approach through history, Birkhäuser (1984), Chapter III: Euler.Google Scholar
8. Pólya, G. and Szegö, G. Problems and theorems in analysis I, Springer (1972) p. 51, pp. 235–236.Google Scholar
9. Scott, J. A. The Euler constant Υ without logarithms, Math. Gaz. (November 1996) pp. 585–586.Google Scholar
10. Bromwich, T. J. I’ A. An introduction to the theory of infinite series (2nd edn.), MacMillan (1959).Google Scholar
11. Hardy, G. H. An introduction to the theory of numbers, Bull. Amer. Math. Soc. 35 (1929) pp. 778–818.Google Scholar
12. Maor, E. e: the story of a number, Princeton University Press (1994).Google Scholar
13. Havil, J. Gamma: exploring Euler’s constant, Princeton University Press (2003).Google Scholar
14. Dunham, W. The calculus gallery, Princeton University Press (2005) p. 54.Google Scholar
15. Klambauer, G. Problems and propositions in analysis, Marcel Dekker (1979) pp. 382–384.Google Scholar
16. Nahin, P. J. Dr. Euler’s fabulous formula, Princeton University Press (2006) pp. 163–173.Google Scholar
17. Lord, N. An amusing sequence of trigonometrical integrals, Math. Gaz. 91 (July 2007) pp. 281–285.Google Scholar
18. Jameson, T. The probability integral by volume of revolution, Math. Gaz. 78 (November 1994) pp. 339–340.Google Scholar
19. Gray, A. Tubes, Addison-Wesley (1990) pp. 253–255.Google Scholar
20. Boros, G. and Moll, V. H. Irresistible integrals, Cambridge University Press (2004).Google Scholar