Closed-form rational approximations of fractional, analog and digital differentiators/integrators

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating $s^{\nu}$, with $-1<\nu<1$, and $(2/T)^{\nu}((z-1)/(z+1))^{\nu}$. The expressions of the coefficients are given in terms of $\nu$ and of the degree $n$ of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition.