Discrete Kontorovich-Lebedev transforms
Classical Analysis and ODEs
2020-06-09 v2
Abstract
Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function is the imaginary unit, and incomplete Bessel functions. Several expansions of suitable functions and sequences in terms of these series and integrals are established. As an application, a Dirichlet boundary value problem in the upper half-plane for inhomogeneous Helmholtz equation is solved.
Cite
@article{arxiv.1908.01392,
title = {Discrete Kontorovich-Lebedev transforms},
author = {Semyon Yakubovich},
journal= {arXiv preprint arXiv:1908.01392},
year = {2020}
}