  The modified q-Bessel functions and the q-Bessel-Macdonald functions of the
first and second kind are introduced. Their definition is based on
representations as power series. Recurrence relations, the q-Wronskians,
asymptotic decompositions and q-integral representations are received. In
addition, the q-Bessel-Macdonald function of kind 3 is determined by its
q-integral representation.
