Integration with Bessel function

[Precursor]

I would like to evaluate the following integral which has a Bessel function $J_{3}(\lambda_{m}r)$, and $\alpha(r)$ is a function.

$$\int^{a}_{0} \alpha(r)rJ_{3}(\lambda_{m}r)dr$$

I'm unsure how to proceed due to the Bessel function. Am I supposed to use a recurrence relation? Which one?

 

[SteamKing]

It depends on what the function α(r) is.

 

[Precursor]

The integral is part of a larger problem, which is to solve the wave equation in polar coordinates. The problem statement does not specify α(r).

Should I just leave the integral as is?

 

[SteamKing]

If this is homework, follow the homework template. We're not here to guess what you should or should no be doing.