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I have the following problem:

I must show that the Bessel function of order [tex]n\in Z [/tex]

[tex]J_n(x)=\int_{-\pi}^\pi e^{ix\sin\vartheta}e^{-in\vartheta}\mathrm{d}\vartheta [/tex]

is a solution of the Bessel differential equation

[tex]x^2\frac{d^2f}{dx^2}+x\frac{df}{dx}+(x^2-n^2)f=0[/tex]

Would be very thankful for some help :-)