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

提出了关于Chapman映射积分\（{\ text {Ch}} \）的指数大气的新解析近似。该表述基于查普曼函数与几类不完整的贝塞尔函数的派生关系。将均匀渐近展开应用于不完整的Bessel函数，使我们能够建立对\（{\ text {Ch}} \}的精确解析近似，胜过已建立的分析结果。这样，可以用导出的逼近以更高的精度代替消耗资源的数值积分。获得的结果可用于大气物理学的各个分支，例如计算大掠射角下指数大气中的光学深度，物理和化学空气动力学，大气光学，电离层建模以及辐射传输理论。