MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.


share|cite|improve this question
This site supports $\TeX$, so why not use it? – Suvrit Dec 18 '12 at 9:41
Also su math.stackexchange… – Jon Dec 18 '12 at 10:20

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.