Fibonacci Sequence and Series by Second Order Difference Operator with Logarithmic Function

Rajiniganth P,Britto Antony Xavier G

doi:10.26524/cm39

Abstract

Fibonacci Sequence and Series by Second Order Difference Operator with Logarithmic Function

Highlights

In 2011, M.Maria Susai Manuel, et al, [7] introduced the generalized α−difference operator as ∆ v(k) = v(k + ) − αv(k) for the real valued function v(k)
Fibonacci and Lucas numbers cover a wide range of interest in modern mathematics as they appear in the comprehensive works of Koshy [6] and Vajda [10]
The k−Fibonacci sequence introduced by Falcon and Plaza [3] depends only on one integer parameter k and is defined as 2∗brittoshc@gmail.com

Summary

Introduction

Corollary 2.8 If v(k), k > n + 2 is a closed form solution of second order difference equation with logarithmic function A closed form solution of the second order difference equation logarithmic function v(k) − αplogkpv(k − p) = kt − αplogkp(k − p)t is p=1 p=1

Results

Conclusion