Convolutions of second order sequences: A direct approach

TL;DR

This paper introduces a direct algebraic method to derive convolution identities for second order sequences, including Horadam sequences and Chebyshev polynomials, distinguishing between different recurrence relations.

Contribution

It presents a novel direct algebraic approach to convolution identities for various second order sequences, expanding the theoretical framework.

Findings

Derived convolution identities for second order sequences

Established a general convolution formula for Horadam sequences

Presented convolution formulas for Chebyshev polynomials

Abstract

Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam sequences. Convolutions for Chebyshev polynomials will also be stated.