  Discrete analogs of the classical Kontorovich-Lebedev transforms are
introduced and investigated. It involves series with the modified Bessel
function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ is the
imaginary unit, and incomplete Bessel functions. Several expansions of suitable
functions and sequences in terms of these series and integrals are established.
As an application, a Dirichlet boundary value problem in the upper half-plane
for inhomogeneous Helmholtz equation is solved.
