Consider the screened Poisson equation $\Delta u(r) - cu(r) = -g(r)$, in a ball (centered at the origin) of radius $R$, with boundary condition $u(R)=0$.
In 3-dimensional space, the Green's function for the above equation is given by
$G(r, R) = \frac{1}{4 \pi r}\frac{\mathrm{sinh}(R-r)\sqrt{c}}{\mathrm{sinh}(R\sqrt{c})}$,
as mentioned in this article.
I am interested in finding a similar expression for this Green's function that generalizes to higher dimensions ($n>3$). So far I have looked into the article's cited source and Duffy's Green's Functions with Applications, but have not been able to locate or derive the general expression for higher dimensions.
I would appreciate any guidance on where and how to find such an expression.