  The Schr\"odinger-Coulomb Sturmian problem in $\mathbb{R}^{N}$,
$N\geqslant2$, is considered in the momentum representation. An integral
formula for the Gegenbauer polynomials, found recently by Cohl
[arXiv:1105.2735], is used to separate out angular variables and reduce an
integral Sturmian eigenvalue equation in $\mathbb{R}^{N}$ to a Fredholm one on
$\mathbb{R}_{+}$. A kernel of the latter equation contains the Legendre
function of the second kind. A symmetric Poisson-type series expansion of that
function into products of the Gegenbauer polynomials, established by Ossicini
[Boll. Un. Mat. Ital. 7 (1952) 315], is then used to determine the
Schr\"odinger-Coulomb Sturmian eigenvalues and associated momentum-space
eigenfunctions. Finally, a relationship existing between solutions to the
Sturmian problem and solutions to a (physically more interesting) energy
eigenvalue problem is exploited to find the Schr\"odinger-Coulomb bound-state
energy levels in $\mathbb{R}^{N}$, together with explicit representations of
the associated normalized momentum-space Schr\"odinger-Coulomb Hamiltonian
eigenfunctions.
