Integrating products of Bessel functions

[appelberry]

Hi guys,

Does anyone have any ideas about an analytical solution for the following integral?

$$\int_{0}^{2\pi}J_{m}\left(z_{1}\cos\theta\right)J_{n}\left(z_{2}\sin\theta\right)d\theta$$

$$J_{m}\left(\right)$$ is a Bessel function of the first kind of order m. Thanks.

 

[g_edgar]

Can you do the special case
$$\int _{0}^{2\,\pi }\!{{\rm J}_0\left(\cos \left( t \right) \right)}\;{dt}$$