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We consider an exactly solvable discretisation of the radial Schr\"odingerequation of the hydrogen atom with l=0. We first examine direct solutions ofthe finite difference equation and remark that the solutions can beanalytically continued entire functions. A recursive expression for thecoefficients in the solution is obtained. The next step is to identify therelated three-term recursion relation for Pollaczek polynomials. One-to-onecorrespondence between the spectral and position representations facilitatesthe evaluation of Pollaczek polynomials corresponding to the discrete spectrum.Finally, we obtain two alternative and explicit expressions for the solutionsof the original difference equation.Comment: 7 pages, no figures, revised version, some minor errors correcte

Explicit representations of Pollaczek polynomials corresponding to an exactly solvable discretization of the hydrogen radial Schrödinger equation