  A concise method of deriving expressions for Gaussian-like solutions of the
paraxial and d'Alembert equations is presented. This method is based on the
Hankel transform. Choosing some Gaussian base functions with slight
modifications of the prefactor all basic beams of cylindrical character can be
easily obtained. This refers to Gaussian, Bessel-Gaussian, modified
Bessel-Gaussian, Laguerre-Gaussian and Kummer-Gaussian (i.e.,
Hypergeometric-Gaussian) beams although potentially other beams can come into
play as well. For instance a new type of a beam that can be derived in this way
is described through the incomplete gamma function so it may be called a
$\gamma$ beam.
