  Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian
beams are considered. Two selected parameters characterizing these beams, with
respect to which the superpositions are constructed, are the topological index
$n$ associated with the orbital angular momentum carried by the beam, and
$\chi$ related to the dilation of the beam. It is shown that, from these modes,
by choosing appropriate weighting factors, it is possible to create a number of
well- and less-known solutions of the paraxial equation: Gaussian (shifted and
non-shifted) beam, $\gamma$ beam, Kummer-Gaussian beam, special hyperbolic
Bessel-Gaussian beam, a certain special Laguerre-Gaussian beam, and generalized
paraxial beams in hyperbolic and regular versions.
