Given $x_{i}$ is a fixed point in [-L,L], $l_{0}$ and $L$ is also positive constant. $|x_{i}-y|$ represent absolute value of $(x_{i}-y)$. define $z=\frac{|x_{i}-y|}{l_{o}}$.
$\mathbf{H_{\alpha}}$ is Struve function. $Y_{\alpha}$ is Bessel function of the second kind. $P_{n}$ is Legendre polynomials.
My question is how to do the following integral?
$$\int_{-\frac{L}{2}}^{\frac{L}{2}}(\frac{\mathbf{H}_{1}(z)}{z}-\frac{2}{\pi z^{2}}-\frac{Y_{0}(z)+Y_{2}(z)}{2})P_{j}(\frac{2y}{L})dy$$
Many Thanks!!