Could some one help me in evaluating this definite integral of Bbessel's function with an exponential function
$$\int_0^1 e^{-ar^2}J_1(\lambda_n r )dr= ?$$
where $\lambda_n$ is any of the roots of $J_1$ and $a$ is a constant.
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2Consider using MathJax for your posts here. Formatting tips here. – StubbornAtom Oct 17 '16 at 18:24
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Perhaps try to integrate $\sum_{m =-\infty}^{\infty} t^m J_m(r) = e^{ r ( t - 1/t)/2}$ and then pick up the coefficient of $t = 1$? – anecdote Oct 17 '16 at 20:11