  The ground state of the Dirac one-electron atom, placed in a weak, static
electric field of definite $2^{L}$-polarity, is studied within the framework of
the first-order perturbation theory. The Sturmian expansion of the generalized
Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825,
erratum: 30 (1997) 2747] is used to derive closed-form analytical expressions
for various far-field and near-nucleus static electric multipole
susceptibilities of the atom. The far-field multipole susceptibilities --- the
polarizabilities $\alpha_{L}$, electric-to-magnetic cross-susceptibilities
$\alpha_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and electric-to-toroidal-magnetic
cross-susceptibilities $\alpha_{\mathrm{E}L\to\mathrm{T}L}$ --- are found to be
expressible in terms of one or two non-terminating generalized hypergeometric
functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the
near-nucleus multipole susceptibilities --- the electric nuclear shielding
constants $\sigma_{\mathrm{E}L\to\mathrm{E}L}$, near-nucleus
electric-to-magnetic cross-susceptibilities
$\sigma_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and near-nucleus
electric-to-toroidal-magnetic cross-susceptibilities
$\sigma_{\mathrm{E}L\to\mathrm{T}L}$ --- involve terminating ${}_{3}F_{2}(1)$
series and for each $L$ may be rewritten in terms of elementary functions.
Exact numerical values of the far-field dipole, quadrupole, octupole and
hexadecapole susceptibilities are provided for selected hydrogenic ions.
Analytical quasi-relativistic approximations, valid to the second order in
$\alpha Z$, where $\alpha$ is the fine-structure constant and $Z$ is the
nuclear charge number, are derived for all types of the far-field and
near-nucleus susceptibilities considered in the paper.
