Accurate analytic approximation for the Chapman grazing incidence function

Abstract A new analytical approximation for the Chapman mapping integral, $${\text {Ch}}$$ Ch , exponential atmospheres is proposed. This formulation based on derived relation of function to several classes incomplete Bessel functions. Application uniform asymptotic expansion functions allowed us establish precise which outperforms established results. In this way resource consuming numerical integration can be replaced by with higher accuracy. The obtained results are useful various branches atmospheric physics such as calculations optical depths in at large grazing angles, physical and chemical aeronomy, optics, ionospheric modeling, radiative transfer theory.