Discrete Lebedev–Skalskaya transforms

Discrete analogs of the Lebedev–Skalskaya transforms are introduced and investigated. It involves series integrals with respect to kernels Re Kα+in(x),Im Kα+in(x),x>0,n∈N,|α|<1, i is imaginary unit Kν(z) modified Bessel function. The corresponding inversion formulas for suitable functions sequences in terms these established when α=±1/2. case α=0 reduces Kontorovich–Lebedev transform.