New biorthogonal sequences generated by index integrals of the weight functions

TL;DR

This paper introduces new biorthogonal sequences derived from index integrals of special functions, utilizing composition orthogonality with differential operators, and explores their properties and connections to generalized Wilson polynomials.

Contribution

It presents novel biorthogonal sequences generated by index integrals of Bessel and gamma functions, expanding the theory of orthogonal polynomials and special functions.

Findings

New biorthogonal sequences constructed from index integrals.

Properties of these sequences and their relation to generalized Wilson polynomials.

Application of composition orthogonality involving differential operators.

Abstract

We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson polynomials are introduced. Some properties are investigated.