A Definite Integration Method for Calculating Inclination Function and Its Derivative

This paper gives a definite integration method for calculating the inclination function and its derivative, which has a very simple expression, and the accuracies as high as 10-15 for the inclination function, and 10-13 for its derivative, comparable with the accuracy of Gooding's method. By through a lot of numerical simulations, it is proved that this method has a good stability and an wide applicable range of inclinations, hence it can be used to calculate the inclination function to the maximum order of Lmax ≤ 50.