Integrating the product of two functions one of which has a positive non-integer power - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T18:28:04Z http://mathoverflow.net/feeds/question/42262 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42262/integrating-the-product-of-two-functions-one-of-which-has-a-positive-non-integer Integrating the product of two functions one of which has a positive non-integer power Olumide 2010-10-15T08:55:41Z 2010-10-15T08:55:41Z <p>I'm looking to integrate several functions having the form</p> <p>$\int_0^T \frac{ sin(\omega \tau) }{\omega} \tau^{2H} d\tau$</p> <p>where $2H \ge 0$ but may not be an integer. I'd like to know if the machinery of fractional calculus (e.g. fractional integration by parts) can be used to integrate such an expression.</p> <p>Thanks.</p> <p>(PS: I'm not quite sure to which category/tag this question belongs.)</p>