Two Methods for Deriving the Recursion Formula of Inclination Function

Two kinds of recursion relations of hypergeometric series were derived, and hereby the Gooding's recursion formula of inclination function. In addition, it was demonstrated that this recursion formula can be derived also on the basis of the recursion relation of Jacobi polynomials. Comparing with the hypergeometric series, the recursion process based on the Jacobi polynomials is much simpler, indicating that the Gooding's method is the recursion of Jacobi polynomials in essence.