Compute $\int_{1}^{\infty} \frac{J^2_{n}(k)}{k^m} dk$

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Question as the title showed,in which J means Bessel functions, n and m are positive integers. How to get the analytic result? Any comment is much appreciated. Many thanks in advance.How to simplify the following formula when $n>2m+1$ and $n$ is odd. enter image description here