Schur parameters and Caratheodory class

The Schur (resp. Caratheodory) class consists of all the analytic functions $f$ on the unit disk with $|f|le 1$ (resp. $Re f>0$ and $f(0)=1$). The Schur parameters $gamma_0,gamma_1,dots (|gamma_j|le 1)$ are known to parametrize the coefficients of functions in the Schur class. By employing a recursive formula for it, we describe the $n$-th coefficient of a Caratheodory function in terms of $n$ independent variables $gamma_1,dots, gamma_n$ with $|gamma_j|le 1.$ The mapping properties of those correspondences are also studied.