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Discrete Lebedev-Skalskaya transforms

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