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arXiv · 1908.01392

Discrete Kontorovich-Lebedev transforms

Semyon Yakubovich
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Abstract

Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ 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.

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Semyon Yakubovich. 2019-08-04. Discrete Kontorovich-Lebedev transforms. https://arxiv.org/abs/1908.01392

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