Jul 6, 2013 #1 A Alan0354 Full Member level 4 Joined Sep 6, 2011 Messages 214 Helped 30 Reputation 60 Reaction score 29 Trophy points 1,308 Activity points 2,709 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
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
Aug 28, 2013 #2 R riso Junior Member level 3 Joined Mar 4, 2002 Messages 26 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 105 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
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