Gaussian integral puzzle

Mathematical Intelligencer

Volumn 31, Issue 3, 2009, Pages 38-41

  Iwasawa, Hirokazu ^a  

^a NONE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84893438136     PISSN: 03436993     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00283-009-9050-1     Document Type: Article

References (9)

1. 2) since high school students are more familiar with the former. But I won't care about this kind of thing any more in the following sections.
2. Peter M. Lee's webpage, "Information on the History of the Normal Law (pdf file)" (http://www.york.ac.uk/depts/ maths/histstat/normal_history.pdf).
3. It gives helpful data on the first appearance of each of the seven ways he gathered to evaluate the Gaussian integral, including most of the methods in the present article.
4. Both iterated integrations in the following are actually valid and have the same value although that's not obvious at all. For this kind of justification, a useful theorem is found.
5. Paul Loya, "Dirichlet and Fresnel Integrals via Iterated Integration", Mathematics Magazine, Vol. 78, No. 1, 2005, pp. 63-67.
6. Martin Aigner and Günter M. Ziegler, Proofs from THE BOOK, 3rd ed., Springer, Berlin 2004, ch. 20.
7. G.N. Watson, Complex Integration and Cauchy's Theorem, Hafner Publishing, New York 1914, p. 79.
8. E.T. Copson, An Introduction to the Theory of Functions of a Complex Variable, Clarendon Press, Oxford 1935, p. 125.
9. When you give up (I'm sorry), you can find a bunch of solutions in Dragoslav S. Mitrinović and Jovan D. Kečkić, The Cauchy Method of Residues, D. Reidel Publishing Company, Dordrecht 1984.