The wave functions for propagation of rotationally symmetric modes in circular gyrotropic waveguides with azimuthal magnetisation (the complex Kummer and Tricomi confluent hypergeometric functions) are studied analytically and numerically. Based on specially compiled tables, families of curves are presented, illustrating the behaviour of both higher transcendental functions. The analysis allows a comprehensive treatment of closed and opened circular guiding structures with radially stratified gyrotropic layers, magnetised azimuthally.