Circular $3D$ Kummer–Gauss beams with the continuous angular index

Analytical expressions in the closed shape for circular $3D$ Kummer–Gauss beams $(cK-G)$ with the continuous angular coefficient $m$ are offered and analyzed. Physical restrictions on possible values of the free parameters of such beams are formulated. Pictorial modeling of beams $(cK-G)$ is fulfilled and shown that the continuous values of an angular coefficient $m$ and complex values of the free parameter $\nu$ are physically possible.