  Discrete analogs of the classical Mehler-Fock transforms are introduced and
investigated. It involves series with the associated Legendre function
$P^\mu_{in-1/2}(x), x > 1,\ {\rm Re} \mu < 1/2, \ n \in \mathbb{N}, i $ is the
imaginary unit, and the so-called incomplete Legendre integrals. Several
expansions of arbitrary functions and sequences in terms of these series and
integrals are established.
