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where latexmath:[ L ] is the length and latexmath:[ R ] the radius of the pillbox, latexmath:[ J_m ] is the m-th Bessel function of the first kind, latexmath:[ x_{mn}^\prime ] is the n-th root of the first derivative of latexmath:[ J_m ], latexmath:[ k_{mn} = \frac{x_{mn}^\prime}{R}] and latexmath:[ \omega = c\cdot\sqrt{k_mn^2 + \frac{p\pi}{L}^2}].
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where latexmath:[ L ] is the length and latexmath:[ R ] the radius of the pillbox, latexmath:[ J_m ] is the m-th Bessel function of the first kind, latexmath:[ x_{mn}^\prime ] is the n-th root of the first derivative of latexmath:[ J_m ], latexmath:[ k_{mn} = \frac{x_{mn}^\prime}{R}] and latexmath:[ \omega = c\cdot\sqrt{k_mn^2 + \left(\frac{p\pi}{L}\right)^2}].
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