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Some infinite sums related to the generalized k-Fibonacci numbers

Year 2022, Issue: 15, 21 - 28, 22.06.2022

Abstract

In this study, some infinite sums related to the generalized k-Fibonacci numbers have been obtained by using infinite sums related to classic Fibonacci numbers and generalized Fibonacci numbers in literature.

References

  • Referans1 Koshy, T. (2001), Fibonacci and Lucas Numbers with Applications, Wiley, New York.
  • Referans2 Falcon S., Plaza A. (2007), On the Fibonacci k-numbers, Chaos, Solitons & Fractals, 32(5), 1615-1624.
  • Referans3 Yosma Z. (2008), Fibonacci and Lucas Numbers, Master's thesis, Graduate School of Natural Sciences, Sakarya University, Sakarya.
  • Referans4 Saba N., Boussayoud, A. (2021), On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solitons & Fractals, vol 146, doi: 10.1016 / j.chaos 2021.110899.2021.
  • Referans5 Chelgham, M., Boussayoud, A. (2021), On the k-Mersenne Lucas numbers, Notes on number theory and discrete mathematics, 27(1), 7-13.
  • Referans6 Saba N., Boussayoud, A., Abderrezzak, A. (2021), Symmetric and generating functions of generalized (p,q) numbers, Kuwait Journal of Science, 48(4).
  • Referans7 Boughaba, S., Boussayoud, A., Saba, N., Kanuri, K. V. V. (2021), A new family of generating functions of binary products of bivariate complex Fibonacci polynomials and Gaussian numbers, Tblisi Mathematical Journal, 14(2), 221-237.
  • Referans8 Taskara N., Uslu K., Gulec H. H. (2010), On the properties of Lucas numbers with binomial coefficients, Applied Mathematics Letters, 23(1), 68-72.
  • Referans9 Gulec H. H., Taskara N., Uslu K. (2013), A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Applied Mathematics and Computation, 220, 482-486.
  • Referans10 Uslu K., Taskara N., Uygun S. (2011), The relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers and the spectral norms of the matrices of involving these numbers, Ars Combinatoria, 102, 183-192.
  • Referans11 Uslu K., Taskara N., Kose H. (2011), The generalized k-Fibonacci and k-Lucas Numbers, Ars Combinatoria, 99, 25-32.
  • Referans12 Uslu K., Taskara N., Gulec H. H. (2011), Combinatorial sums of generalized Fibonacci and Lucas numbers, Ars Combinatoria, 99, 139-147.
  • Referans13 Uslu K., Teke M. (2022), Infinite sums related to the generalized Fibonacci numbers, Advances and Applications in Discrete Mathematics, 29(1), 85-96.
Year 2022, Issue: 15, 21 - 28, 22.06.2022

Abstract

References

  • Referans1 Koshy, T. (2001), Fibonacci and Lucas Numbers with Applications, Wiley, New York.
  • Referans2 Falcon S., Plaza A. (2007), On the Fibonacci k-numbers, Chaos, Solitons & Fractals, 32(5), 1615-1624.
  • Referans3 Yosma Z. (2008), Fibonacci and Lucas Numbers, Master's thesis, Graduate School of Natural Sciences, Sakarya University, Sakarya.
  • Referans4 Saba N., Boussayoud, A. (2021), On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solitons & Fractals, vol 146, doi: 10.1016 / j.chaos 2021.110899.2021.
  • Referans5 Chelgham, M., Boussayoud, A. (2021), On the k-Mersenne Lucas numbers, Notes on number theory and discrete mathematics, 27(1), 7-13.
  • Referans6 Saba N., Boussayoud, A., Abderrezzak, A. (2021), Symmetric and generating functions of generalized (p,q) numbers, Kuwait Journal of Science, 48(4).
  • Referans7 Boughaba, S., Boussayoud, A., Saba, N., Kanuri, K. V. V. (2021), A new family of generating functions of binary products of bivariate complex Fibonacci polynomials and Gaussian numbers, Tblisi Mathematical Journal, 14(2), 221-237.
  • Referans8 Taskara N., Uslu K., Gulec H. H. (2010), On the properties of Lucas numbers with binomial coefficients, Applied Mathematics Letters, 23(1), 68-72.
  • Referans9 Gulec H. H., Taskara N., Uslu K. (2013), A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Applied Mathematics and Computation, 220, 482-486.
  • Referans10 Uslu K., Taskara N., Uygun S. (2011), The relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers and the spectral norms of the matrices of involving these numbers, Ars Combinatoria, 102, 183-192.
  • Referans11 Uslu K., Taskara N., Kose H. (2011), The generalized k-Fibonacci and k-Lucas Numbers, Ars Combinatoria, 99, 25-32.
  • Referans12 Uslu K., Taskara N., Gulec H. H. (2011), Combinatorial sums of generalized Fibonacci and Lucas numbers, Ars Combinatoria, 99, 139-147.
  • Referans13 Uslu K., Teke M. (2022), Infinite sums related to the generalized Fibonacci numbers, Advances and Applications in Discrete Mathematics, 29(1), 85-96.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Kemal Uslu 0000-0001-6265-3128

Mustafa Teke 0000-0001-9516-8460

Early Pub Date June 17, 2022
Publication Date June 22, 2022
Submission Date February 25, 2022
Acceptance Date March 7, 2022
Published in Issue Year 2022 Issue: 15

Cite

APA Uslu, K., & Teke, M. (2022). Some infinite sums related to the generalized k-Fibonacci numbers. Journal of New Results in Engineering and Natural Sciences(15), 21-28.