Based on a discussion on the analytical properties of the complex function Fα(y)=∫0(ωph-α)(ω2y)/(ω2y+1)g(ω)dω, we suggest that the partial sum of the Tc series solution proposed by Wu Hang-sheng et al., as an approximate expression for superconducting critical temperature, may still work fairly well within certain range of 1/λ greater thanthe radius of convergence which is limited by the singular point zph. However, the error of the expression that depends upon the highfrequency behavior of the effective phonon spectral g(ω), can not be made infinitely small.