More generalized k(ε)-Fibonacci sequence, series, and its applications-Reference-Cited by-同舟云学术

More generalized k(ε)-Fibonacci sequence, series, and its applications

Published:2024-01-01 Issue:1 Volume:14 Page:
ISSN:2158-3226
Container-title:AIP Advances
language:en
Short-container-title:

Author:

P Rajiniganth¹^ORCID,T Aparna²^ORCID,Khan Ilyas³^ORCID,K Suresh⁴^ORCID

Affiliation:

1. Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University 1 , Samayapuram, Tiruchirapalli, Tamil Nadu 621112, India

2. Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University 2 , Samayapuram, Tiruchirapalli, Tamil Nadu 621112, India

3. Department of Mathematics, College of Science, Al-Zulfi, Majmaah University 3 , Al-Majmaah 11952, Saudi Arabia

4. Department of Mathematics, St. Joseph’s College of Engineering 4 , Old Mahabalipuram Road, Semmancheri, Chennai, Tamilnadu 600 119, India

Abstract

In this study, we present a generalized higher-order delta operator with the co-efficient of falling factorial and its inverse, both of which allow us to get more generalized k(ε)-Fibonacci sequences along with their sums, a few theorems, and some intriguing conclusions regarding the sum of more generalized terms of k(ε)-Fibonacci sequences with falling factorial. In addition, the n-fold Fibonacci ratio and a few applications in life sciences and crystal growth were presented in the work. In addition, suitable examples are presented using MATLAB to show our results.

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/adv/article-pdf/doi/10.1063/5.0180627/18931195/015233_1_5.0180627.pdf

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