  A double covering of the proper orthochronous Lorentz group is understood as
a complexification of the special unimodular group of second order (a double
covering of the 3-dimensional rotation group). In virtue of such an
interpretation the matrix elements of finite-dimensional representations of the
Lorentz group are studied in terms of hyperspherical functions. Different forms
of the hyperspherical functions related to other special functions
(hypergeometric series, generalized spherical functions, Jacobi functions,
Appell functions) are considered. It is shown that there is a close
relationship between hyperspherical functions and physical fields defined
within $(j,0)\oplus(0,j)$ representation spaces. Recurrence relations between
hyperspherical functions are given.
