Vol. 5 No. 2 (2021): Vol 5, Iss 2, Year 2021
Articles

Advanced fibonacci sequence and its sum by second order variable co-efficient difference operator

Rajiniganth P
Department of Mathematics, R.M.K Engineering College, Kavaraipettai-601206, Tamil Nadu, India.
Britto Antony Xavier G
Department of Mathematics, Sacred Heart College, Tirupattur - 635601, Tamil Nadu, India.
Published December 20, 2021
Keywords
  • Difference operator variable co-efficient, Fibonacci sequence, Closed form solution, Fibonacci summation
How to Cite
P, R., & G, B. A. X. (2021). Advanced fibonacci sequence and its sum by second order variable co-efficient difference operator. Journal of Computational Mathematica, 5(2), 92 - 101. https://doi.org/10.26524/cm112

Abstract

We introduce a second order difference operator with specific powers of variable co-efficient and its inverse in this study, which allows us to derive the (α1tr1, α2tr2 )-Fibonacci sequence and its summation. This series is known as the Fibonacci sequence with variable co-efficients (VCFS). On the sum of the terms of the variable co-efficient Fibonacci sequence, some theorems and intriguing findings are generated. To demonstrate our findings, appropriate instances are
presented.

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