Algebraic methods, Bender-Wu formulas, and continued fractions at large order for charmonium

A special coordinate realization of the Lie algebra so(4,2) is used to reformulate the perturbation problem of a hydrogen atom in a linear radial potential over a complete and discrete Sturmian basis. In this way, the Rayleigh-Schrödinger coefficients $E_{\mathrm{NLM}}^{\left(n\right)}$ may be calculated to arbitrarily high order for any state. The large-order behavior of these coefficients is determined by Bender-Wu WKB theory. A general formula for the large-order behavior of the coefficients $c_n^{\mathrm{NLM}}$ of the Stieltjes continued-fraction representations of these perturbation expansions is given and related to that of the $E_{\mathrm{NLM}}^{\left(n\right)}$.