Two-Center Integrals over Solid Spherical Harmonics

One‐electron, two‐center integrals (and the corresponding one‐center case) are evaluated for integrals of the type $${\displaystyle \int }{\mathrm{[N,L,M]}}_a\frac{r_b^{N^{\prime }}{P}_{L^{\prime }}^{{\mathrm{|M}}^{\prime }|}(\cos {\theta }_b)}{r_b^{L^{\prime }\text{+1}}}\left\{\begin{array}{c}\cos {\mathrm{|M}}^{\prime }{\mathrm{|\phi }}_b\\ \\ \sin {\mathrm{|M}}^{\prime }{\mathrm{|\phi }}_b\end{array}\right\}\mathrm{d\tau }$$ arising in electromagnetic interactions. The Fourier convolution theorem method is employed and specific results are obtained for N′=0 and N′=2 in terms of an F function and recursion formulas. All cases up to L′=3 are evaluated in terms of the F functions and in terms of elementary functions.