  The normalization of energy divergent Weber waves and finite energy
Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used
to derive the integral relations between circular, elliptic, and parabolic
waves and to present the Bessel and Mathieu wave decomposition of the Weber
waves. The efficiency to approximate a Weber-Gauss beam as a finite
superposition of Bessel-Gauss beams is also given.
