  The stationary states of the half-line Coulomb potential are described by
quantum-mechanical wavefunctions which are controlled by the Laguerre
polynomials $L_n^{(1)}(x$). Here we first calculate the $q$th-order frequency
or entropic moments of this quantum system, which is controlled by some
entropic functionals of the Laguerre polynomials. These functionals are shown
to be equal to a Lauricella function
$F_A^{(2q+1)}(\frac{1}{q},...,\frac{1}{q},1)$ by use of the
Srivastava-Niukkanen linearization relation of Laguerre polynomials. The
resulting general expressions are applied to obtain the following
information-theoretic quantities of the half-line Coulomb potential:
disequilibrium, Renyi and Tsallis entropies. An alternative and simpler
expression for the linear entropy is also found by means of a different method.
Then, the Shannon entropy and the LMC or shape complexity of the lowest and
highest (Rydberg) energetic states are explicitly given; moreover, sharp
information-theoretic-based upper bounds to these quantities are found for
general physical states. These quantities are numerically discussed for the
ground and various excited states. Finally, the uncertainty measures of the
half-line Coulomb potential given by the information-theoretic lengths are
discussed.
