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journal article·2024-01-01Open access

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

Rajiniganth P, Aparna T, Ilyas Khan, Suresh K

AIP Advances· Volume 14· Issue 1
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Source abstract

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.
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Research context

OpenAlex topics: Advanced Mathematical Theories and Applications · Fractal and DNA sequence analysis · Quasicrystal Structures and Properties

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

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

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

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

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

References (21)

Show source-provided references
1. Fundamentals of a new kind of mathematics based on the golden section10.1016/j.chaos.2005.05.008 ↗
2. Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers10.1016/j.amc.2012.11.030 ↗
3. On the (k, p)-Fibonacci numbers10.3390/math9070727 ↗
4. Some interpretations of the (k, p)-Fibonacci numbers
5. A new generalization of fibonacci sequence and extended Binet’s formula10.1515/integ.2009.051 ↗
6. On The properties of k-Fibonacci numbers
7. On the complex k-Fibonacci numbers10.1080/23311835.2016.1201944 ↗
8. Fibonacci, quasicrystals and the beauty of flowers10.4161/psb.22417 ↗
9. Some formulae for the Fibonacci sequence with generalizations
10. Fibonacci numbers and computer algorithms10.1080/07468342.1987.11973055 ↗
11. 2001
12. On characteristic polynomial of higher order generalized Jacobsthal numbers10.1186/s13662-019-2327-6 ↗
13. The k-Fibonacci sequence and the pascal 2-triangle10.1016/j.chaos.2006.10.022 ↗
14. Metallic phase with long-range orientational order and no translational symmetry10.1103/PhysRevLett.53.1951 ↗
15. The golden shofar10.1016/j.chaos.2005.01.057 ↗
16. Theory of Binet formulas for Fibonacci and lucas p-numbers10.1016/j.chaos.2005.04.106 ↗
17. The golden algebraic equations10.1016/j.chaos.2005.04.107 ↗
18. On the characteristic polynomial of (k, p)-Fibonacci sequence10.1186/s13662-020-03186-8 ↗
19. 1989
20. Some properties of Fibonacci and Chebyshev polynomials10.1186/s13662-015-0420-z ↗
21. (2, k)-distance Fibonacci polynomials10.3390/sym13020303 ↗