Need information in deriving first integral of Bessel's function.

[Alan0354]

Can anyone give me the proof or point me to a link to derive this First Integral of Bessel's Function.

\[J_n(x)=\frac{j^{-n}}{\pi}\int_0^{\pi}\cos(n\phi)e^{jx\cos \phi}d\phi\]

I have been searching all over and can't find the derivation. In fact, other than some basic Bessel's identities that is shown in one PDE book, I have yet to find anything.

Thanks

 

[riso]

Try to use W.Mathematica or site _http://www.wolframalpha.com/input/?i=integrate+%28cos%28x%29+exp%28I+x+cos%28x%29%29%29+from+x%3D0+to+Pi