Generalizations of Fibonacci-Lucas inverse tangent summation identities of Hoggatt and Ruggels

TL;DR

This paper generalizes inverse tangent summation identities involving Fibonacci and Lucas numbers, providing new identities and expanding the mathematical understanding of these sequences.

Contribution

It introduces generalized inverse tangent identities related to Fibonacci and Lucas numbers, extending previous specific cases.

Findings

New inverse tangent identities involving Fibonacci and Lucas numbers

Generalized formulas that encompass previous identities

Enhanced mathematical framework for inverse tangent sums

Abstract

We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities involving the Fibonacci and Lucas numbers.