- #1
maddogtheman
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Homework Statement
The Bessel function generating function is
[tex]
e^{\frac{t}{2}(z-\frac{1}{z})} = \sum_{n=-\infty}^\infty J_n(t)z^n
[/tex]
Show
[tex]
J_n(t) = \frac{1}{\pi} \int_0^\pi cos(tsin(\vartheta)-n\vartheta)d\vartheta
[/tex]
Homework Equations
The Attempt at a Solution
So far I have been able to use an analytic function theorem to write
[tex]
J_n(t)=\frac{1}{2\pi i} \oint e^{\frac{t}{2}(z-\frac{1}{z})}z^{-n-1}dz
[/tex]
(we are required to use this)
But now I have no idea where to go from here.
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