We have determined the first few coefficients of the previously derived Tseries. The critical temperature evaluated by means of our series formula is then compared with those from the formula of Allen and Dynes and with numerical solutions of Eliashberg’s equation. The results suggest that when it is convergent, our Tseries yields values for superconducting critical temperatures, which are closer to the numerical solutions than Allen and Dynes’ formula.We present also a way to estimate the radius of convergence of our Tseries solution.