Integrating the product of two functions one of which has a positive non-integer power

2010-10-15T08:55:41Z

I'm looking to integrate several functions having the form

$\int_0^T \frac{ sin(\omega \tau) }{\omega} \tau^{2H} d\tau$

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.

Thanks.

(PS: I'm not quite sure to which category/tag this question belongs.)

Integrating the product of two functions one of which has a positive non-integer power - MathOverflow

Integrating the product of two functions one of which has a positive non-integer power