Kummer–Gaussian scalar astigmatic three-dimensional light beams

The formalism for the description of paraxial $3D$ Gaussian-like light Kummer–Gaussian beams by a simple astigmatism is offered. Conditions of their physical realizability are formulated. New types of Kummer–Gaussian beams are found. Such beams are presented by Gaussian product on Kummer function of a complex argument and a nonnegative integer index $n$.