Discrete index transforms with Bessel and modified Bessel functions

TL;DR

This paper introduces and investigates discrete index transforms involving Bessel and modified Bessel functions, establishing inversion theorems for specific classes of functions and sequences.

Contribution

It presents new discrete index transforms with Bessel functions and proves their inversion formulas, expanding the mathematical tools available for discrete analysis.

Findings

Inversion theorems for the new transforms are established.

The transforms are applicable to specific classes of functions and sequences.

The paper provides foundational properties of these discrete index transforms.

Abstract

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.