Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

A general solution of RG equations in the framework of background perturbation theory is written in the large-N _c limit. A simplified (model) approximation to the general solution is suggested that allows β(α) and α(s) to be written to any loop order. The resulting α _B (Q²) coincides asymptotically at large |Q²| with standard (free) α _s , saturates at small Q²≥0, and has poles at timelike Q² in agreement with analytic properties of physical amplitudes in the large-N _c limit.