1. Jul 2, 2011

### jayryu

hello,everyone
i want to know how to solve this bessel function integrals:

\int_{0}^{R} J_m-1(ax)*J_m+1 (ax)*x dx
where J_m-1 and J_m+1 is the Bessel function of first kind, and a is a constant.

thanks.

2. Jul 2, 2011

### DuncanM

Is this what you meant to post?

$$\int_{0}^{R} J_{m-1}(ax)*J_{m+1} (ax)*x \ dx$$

I am not an expert on Bessel functions, but isn't there an identity that you can use to simplify this expression? Something like

$$J_{m+1} = Some \ function \ of \ J_m$$

In other words, each successive Bessel function can be defined in terms of its predecessor. For example,

J1 = some function of J0,
J2 = some function of J1,
J3 = some function of J2,
J4 = some function of J3,
etc.

If you can find this identity, you should be able to simplify your integral.

3. Jul 2, 2011

### LCKurtz

Last edited by a moderator: Apr 26, 2017
4. Jul 2, 2011

### jayryu

Last edited by a moderator: Apr 26, 2017
5. Jul 2, 2011

### jayryu

yes,it is.thanks for your suggestions.i have solved it.