Identities and Generating Functions of Products of Generalized Fibonacci numbers, Catalan and Harmonic Numbers

TL;DR

This paper explores properties and identities of generalized Fibonacci, Lucas, Catalan, and harmonic numbers, deriving new identities and generating functions for their products and convolutions.

Contribution

It introduces new identities and generating functions for products of generalized Fibonacci, Lucas, Catalan, and harmonic numbers, extending classical Fibonacci identities.

Findings

Derived new identities for generalized Fibonacci and Lucas numbers.

Established generating functions for products and convolutions of these sequences.

Extended classical Fibonacci identities to generalized sequences.

Abstract

We considered the properties of generalized Fibonacci and Lucas numbers class. The analogues of well-known Fibonacci identities for generalized numbers are obtained. We gained a new identity of product convolution of generalized Fibonacci and Lucas numbers. We wrote down generating functions of generalized Fibonacci and Lucas numbers products, their multisections, harmonic numbers and Catalan numbers.