Solutions of the wave equation in parabolic rotary coordinates. I. 3D Kummer–Kummer light beams with the continuous angular index

Analytical expressions in the closed form for nonparaxial and paraxial 3D Kummer–Kummer (K-K) beams with continuous angular index $m$ in parabolic rotary coordinates are offered and analyzed. Physical restrictions on possible values of the free parameters of such beams are formulated.