Numerically satisfactory solutions of hypergeometric recursions

Each family of Gauss hypergeometric functions $f_n = 2F_1(a+epsilon 1n,b+epsilon 2n;c+epsilon 3n;z), nin Z$, for fixed epsilon_j = 0,pm 1$ (not all epsilon j equal to zero) satisfies a second order linear difference equation of the form $A_n f_{n-1} + B_n f_n + C_n f_{n+1} = 0$. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different epsilon_j values) can be transformed into each other. In this way, only with four basic difference equations all other cases can be obtained. For each of these recurrences, we give pairs of numerically satisfactory solutions in the regions in the complex plane where $|t_1| ot |t_2|, t_1 and t_2$ being the roots of the characteristic equation.