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 $\mathrm{Re}{K}_{\alpha +in}(x),\mathrm{Im}{K}_{\alpha +in}(x),x>0,n\in \mathbb{N},|\alpha |<1,i$ 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.