2020/08/30 by Yakubovich, Semyon
#33C10 #42A16 #44A15 #45A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.13263
Discrete analogs of the Lebedev-Skalskaya transforms are introduced and investigated. It involves series and integrals with respect to the kernels \rm Re Kα+in(x), \rm Im Kα+in(x), x >0, n ∈ ℕ, |α| < 1, i is the imaginary unit and Kν(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= ± 1/2. The case α=0 reduces to the Kontorovich-Lebedev transform.