Discrete Lebedev's index transforms

TL;DR

This paper introduces and investigates discrete versions of Lebedev transforms involving modified Bessel functions, establishing new expansions of functions and sequences using series and integrals with Bessel functions.

Contribution

It presents novel discrete Lebedev index transforms and derives new expansions involving modified and incomplete Bessel functions.

Findings

Introduction of discrete Lebedev transforms

Derivation of function and sequence expansions

Use of series and integrals with Bessel functions

Abstract

Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the modified and incomplete Bessel functions are established.