\[\frac{{H^{\pm}_{\ell}}'}{{H^{\pm}_{\ell}}}=c\pm\frac{\mathrm{i}}{\rho}\cfrac{%
ab}{2(\rho-\eta\pm\mathrm{i})+\cfrac{(a+1)(b+1)}{2(\rho-\eta\pm 2\mathrm{i})+%
\cdots}},\]