# How to solve this Bessel integral?

1. Sep 2, 2008

### vvthuy

Hi,

Do you have any idea to solve this integral?

\int^{\phi_{1}}_{\phi_{2}} exp[j cos(x)] dx

where \phi_{1} and \phi_{2} are an arbitrary angles. If \phi_{1}=\pi and \phi_{2}=0, the answer for this integral is a Bessel function.

Thanks,

Viet.

2. Sep 3, 2008

### Mute

Use the identity

$$e^{ iz\cos\phi} = \sum_{s=-\infty}^{\infty}i^sJ_s(z)e^{is\phi}$$

3. Sep 4, 2008

### vvthuy

Thank you very much. Do you have the reference for this equation since I do not find it in my mathematical books?

4. Sep 4, 2008