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Asymptotic behavior of functions, asymptotic series and related topics

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Asymptotic Expansion of Bessel Function Integral

I have an integral: $$I(y) = \int_0^\infty \frac{xJ_1(yx)^2}{\sinh(x)^2}\ dx $$ and would like to asymptotically expand it as a series in $1/y$. Does anyone know how to do this? By numerically computi …
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