  The pseudospherical functions on one-sheet, two-dimensional hyperboloid are
discussed. The simplest method of construction of these functions is introduced
using the Fock space structure of the representation space of the su(1,1)
algebra. The pseudospherical functions with half-integer order are
investigated. The counterparts of the Legendre functions for the hyperboloid
are introduced and a new class of pseudospherical functions is found.
