- #1
yungman
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I am studying Bessel Function in my antenna theory book, it said:
[tex]\pi j^n J_n(z)=\int_0^{\pi} \cos(n\phi)e^{+jz\cos\phi}d\phi[/tex]I understand:
[tex]J_m(z)=\frac{1}{2\pi}\int_0^{2\pi}e^{j(z\sin\phi-m\theta)} d\theta[/tex]
Can you show me how do I get to
[tex]\pi j^m J_m(z)=\int_0^{\pi} \cos(m\theta)e^{+jz\cos\theta}d\theta[/tex]
I tried ##e^{jm\theta}=\cos m\theta +j\sin m \theta## but it is not easy. Please help.
[tex]\pi j^n J_n(z)=\int_0^{\pi} \cos(n\phi)e^{+jz\cos\phi}d\phi[/tex]I understand:
[tex]J_m(z)=\frac{1}{2\pi}\int_0^{2\pi}e^{j(z\sin\phi-m\theta)} d\theta[/tex]
Can you show me how do I get to
[tex]\pi j^m J_m(z)=\int_0^{\pi} \cos(m\theta)e^{+jz\cos\theta}d\theta[/tex]
I tried ##e^{jm\theta}=\cos m\theta +j\sin m \theta## but it is not easy. Please help.
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