Two Finite Classes of Orthogonal Functions

TL;DR

This paper introduces two new classes of finite orthogonal functions derived from Fourier transforms of symmetric finite orthogonal polynomials, establishing their orthogonality relations.

Contribution

It presents novel classes of finite orthogonal functions and derives their orthogonality relations using Fourier analysis and Parseval's identity.

Findings

Two new classes of orthogonal functions are defined.

Orthogonality relations are established for these functions.

Abstract

By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval's identity.