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The exponential integral function is defined by $$ Ei(z) = \int_{-\infty}^z dw \frac{e^w}{w} \,.$$ Away from the negative real axis the exponential integral function has a Taylor series about $z=0$: $$...

I am considering the following ODE \begin{equation} \begin{split} &\frac{d^2}{dy^2}u + \frac{\alpha}{(1+y^2)^{\frac{r}{2}}}u = \delta(y)\\ &\lim_{|y|\to \infty}u(y) = 0. \end{split} \end{...