On the orthogonality and convolution orthogonality via the Kontorovich-Lebedev transform

TL;DR

This paper explores orthogonality and convolution orthogonality using the Kontorovich-Lebedev transform, introducing new classes of orthogonal polynomials and functions with detailed integral and explicit representations.

Contribution

It introduces new classes of orthogonal polynomials and functions based on the Kontorovich-Lebedev transform, with comprehensive integral and orthogonality relations.

Findings

New classes of orthogonal polynomials identified

Integral representations established for these classes

Orthogonality relations derived explicitly

Abstract

Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral representations, orthogonality relations and explicit expressions are established.