  Considering the kernel of an integral operator intertwining two realizations
of the group of motions of the pseudo-Euclidian space, we derive two formulas
for series containing Whittaker's functions or Weber's parabolic cylinder
functions. We can consider this kernel as a special function. Some particular
values of parameters involved in this special function are found to coincide
with certain variants of Bessel functions. Using these connections, we also
establish some analogues of orthogonality relations for Macdonald and Hankel
functions.
