  Square grid circle patterns with prescribed intersection angles, mimicking
holomorphic maps z^a and log(z) are studied. It is shown that the corresponding
circle patterns are imbedded and described by special separatrix solutions of
discrete Painleve and Riccati equations. General solution of this Riccati
equation is expressed in terms of the hypergeometric function. Global
properties of these solutions, as well as of the discrete z^a and log(z), are
established.
