Discrete Lebedev-Skalskaya transforms

Abstract

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