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Integrating expressions of the form and others

Published online by Cambridge University Press:  23 January 2015

J. Trainin
J. Trainin*
Affiliation:
Edificio La Roca 27, Paseo del Altillo 11, 18690 Almuñécar, Granada, Spain
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Extract

In an earlier communication to the Gazette [1], the authors in effect showed, in a somewhat complicated manner, how to evaluate the integral One can show in a simpler manner, however, how to evaluate, for integers n and m, a more general integral of the form where n ≥ m, provided that if m = 1, then n is odd.

In addition, the final section to this article shows how to extend the procedure to include integrals for which m does not even have to be an integer, and also how to integrate where such an integral converges.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 530 , July 2010 , pp. 216 - 223
Copyright
Copyright © The Mathematical Association 2010

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References

1. Luo, Qiu-Ming, Guo, Bai-ni and Qi, Feng, Evaluation of a class of improper integrals of the first kind, Math. Gaz. 87 (November 2003) pp. 534–539.CrossRefGoogle Scholar
2. Weisstein, Eric W., “Frullani's Integral“, MathWorld, http:/mathworld.wolfram.com/FrullanisIntegral.html Google Scholar
3. Abramowitz, & Stegun, , Handbook of mathematical functions (table of definite integrals), Dover (1974).Google Scholar
4. Volkovyskii, Lunts & Aramanovich, , A collection of problems on complex analysis, Dover (1991) Problem 873.Google Scholar