More generalized k(ε)-Fibonacci sequence, series, and its applications
Rajiniganth P,
Aparna T,
Ilyas Khan,
Suresh K
Affiliations
Rajiniganth P
Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University, Samayapuram, Tiruchirapalli, Tamil Nadu 621112, India
Aparna T
Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University, Samayapuram, Tiruchirapalli, Tamil Nadu 621112, India
Ilyas Khan
Department of Mathematics, College of Education, Majmmah University, Al-Majmaah 11952, Saudi Arabia
Suresh K
Department of Mathematics, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Semmancheri, Chennai, Tamilnadu 600 119, India
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.
