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The stationary states of the half-line Coulomb potential are described byquantum-mechanical wavefunctions which are controlled by the Laguerrepolynomials $L_n^{(1)}(x$). Here we first calculate the $q$th-order frequencyor entropic moments of this quantum system, which is controlled by someentropic functionals of the Laguerre polynomials. These functionals are shownto be equal to a Lauricella function$F_A^{(2q+1)}(\frac{1}{q},...,\frac{1}{q},1)$ by use of theSrivastava-Niukkanen linearization relation of Laguerre polynomials. Theresulting general expressions are applied to obtain the followinginformation-theoretic quantities of the half-line Coulomb potential:disequilibrium, Renyi and Tsallis entropies. An alternative and simplerexpression 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 andhighest (Rydberg) energetic states are explicitly given; moreover, sharpinformation-theoretic-based upper bounds to these quantities are found forgeneral physical states. These quantities are numerically discussed for theground and various excited states. Finally, the uncertainty measures of thehalf-line Coulomb potential given by the information-theoretic lengths arediscussed.

Entropic functionals of Laguerre polynomials and complexity properties of the half-line Coulomb potential