most recent 30 from http://mathoverflow.net 2013-05-25T09:23:45Z http://mathoverflow.net/feeds/question/116682 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116682/integrate-square-of-bessel-1st-and-2nd-kind zam 2012-12-18T04:59:53Z 2012-12-18T10:16:41Z

<p>Has anyone ever solved the integral of square of Bessel and Neumann functions? This is for standing wave analysis on a cylindrical object.</p> <p>I need to integrate $(AJ(kr) + BY(kr))^2$ from $r=a$ to $r=b$, where $$A = \frac{-Y'(ka) V}{J'(ka)Y'(kb) - J'(kb)Y'(ka)}$$ and $$B= \frac{J'(ka) V}{J'(ka)Y'(kb) - J'(kb)Y'(ka)},$$ where $V$ is the velocity constant, and $a$ and $b$ are the radii of the torus.</p> <p>$J(kr)$ is the Bessel function of the 1st kind and $Y(kr)$ is of the 2nd kind. $J'(\,\cdot\,)$ and $Y'(\,\cdot\,)$ are the first derivatives of these functions.</p> <p>Thanks.</p>