I need to solve the following integral
\begin{equation} \int_{0}^{\infty} Y_1\big(\sigma \cdot (r-a) \cdot \sin(\theta) \big) e^{-\sigma^2 \nu t} d\sigma \end{equation}
where $Y_1(x)$ is the Bessel Function of the second kind. I was unable to solve it directly in Maple. Can anyone help me to solve it?
From the above integral, I want to calculate the following \begin{equation} \frac{d}{dr} \int_{0}^{\infty} r \ Y_1\big(\sigma \cdot (r-a) \cdot \sin(\theta) \big) \ e^{-\sigma^2 \nu t} \ d\sigma \end{equation}
So any solution to the above integrals will solve my problem. I appreciate your help.