Discrete index transformations with squares of Bessel functions

TL;DR

This paper introduces and studies discrete index transforms involving squares of Bessel functions, providing inversion theorems for specific classes of functions and sequences.

Contribution

It presents new discrete index transforms with squares of Bessel functions and establishes their inversion formulas, expanding the mathematical tools available for such transforms.

Findings

Introduced discrete index transforms with Bessel function squares

Proved inversion theorems for these transforms

Analyzed properties for specific function classes

Abstract

Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.