# integrate square of bessel 1st and 2nd kind

Has anyone ever solved the integral of square of Bessel and Neumann functions? This is for standing wave analysis on a cylindrical object.

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.

$J(kr)$ 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.

Thanks.

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This site supports $\TeX$, so why not use it? –  Suvrit Dec 18 '12 at 9:41
Also su math.stackexchange math.stackexchange.com/questions/261289/… –  Jon Dec 18 '12 at 10:20