  We studied a novel family of paraxial laser beams forming an overcomplete yet
nonorthogonal set of modes. These modes have a singular phase profile and are
eigenfunctions of the photon orbital angular momentum. The intensity profile is
characterized by a single brilliant ring with the singularity at its center,
where the field amplitude vanishes. The complex amplitude is proportional to
the degenerate (confluent) hypergeometric function, and therefore we term such
beams hypergeometric gaussian (HyGG) modes. Unlike the recently introduced
hypergeometric modes (Opt. Lett. {\textbf 32}, 742 (2007)), the HyGG modes
carry a finite power and have been generated in this work with a liquid-crystal
spatial light modulator. We briefly consider some sub-families of the HyGG
modes as the modified Bessel Gaussian modes, the modified exponential Gaussian
modes and the modified Laguerre-Gaussian modes.
