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Year 2024, Volume: 7 Issue: 2, 71 - 79
https://doi.org/10.33434/cams.1444712

Abstract

References

  • [1] A. F. Horadam, Special properties of the sequenceWn(a;b; p;q) , Fibonacci Quart., 5(5) (1967), 424-434.
  • [2] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, 3(3) (1965), Fibonacci Quart., 161-176.
  • [3] A. F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly, 68(5) (1961), 455-459.
  • [4] Z. Akyuz, S. Halici, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat., 42(4) (2013), 431-435.
  • [5] Z. Akyuz, S. Halici, Some identities deriving from the nth power of a special matrix, Adv. Difference Equ., (2012(1)), 1-6.
  • [6] C. K. Cook, Some sums related to sums of Oresme numbers, In Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications, (2004), 87-99.
  • [7] James Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2x2 matrix, Integers, 4 (2004), A19.
  • [8] N. Oresme, Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961).
  • [9] A. F. Horadam, Oresme Numbers, Fibonacci Quart., 12(3) (1974), 267- 271.
  • [10] G. Y. Senturk, N. Gurses, S. Yuce, A new look on Oresme numbers: dual-generalized complex component extension, In Conference Proceeding Science and Technology, 1(1) (2018), 254-265.
  • [11] G. Cerda Morales, Oresme polynomials and their derivatives, arXiv preprint arXiv:1904.01165, (2019).
  • [12] S. Halici, E. Sayin, Z. B. Gur, k- Oresme numbers and k- Oresme numbers with negative indices, ICMASE (2022), 211-223.
  • [13] S. Halici, E. Sayin, On some k􀀀 Oresme hybrid numbers, Util. Math., 120, (2023), 1-11.
  • [14] S. Halici, Z. B. Gur, E. Sayin, k- Oresme polynomials and their derivatives, ICMASE, (2022), 201-210.
  • [15] S. Halici, Z. B. Gur, On some derivatives of k- Oresme polynomials, Bulletin of IMVI, 13(1) (2023), 41-50.
  • [16] Y. Soykan, A study on generalized p- Oresme numbers, Asian Journal of Advanced Research and Reports, 15(7) (2021), 1-25.

On Some k-Oresme Polynomials with Negative Indices

Year 2024, Volume: 7 Issue: 2, 71 - 79
https://doi.org/10.33434/cams.1444712

Abstract

In this study, \textit{k-} Oresme polynomials with negative indices, which are the generalization of Oresme polynomials, were examined and defined. By examining the algebraic properties of recently defined polynomial sequences, some important identities were given. The matrices of negative indices \textit{k-} Oresme polynomials was defined. Some sum formulas were given according to this definition.

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References

  • [1] A. F. Horadam, Special properties of the sequenceWn(a;b; p;q) , Fibonacci Quart., 5(5) (1967), 424-434.
  • [2] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, 3(3) (1965), Fibonacci Quart., 161-176.
  • [3] A. F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly, 68(5) (1961), 455-459.
  • [4] Z. Akyuz, S. Halici, On some combinatorial identities involving the terms of generalized Fibonacci and Lucas sequences, Hacet. J. Math. Stat., 42(4) (2013), 431-435.
  • [5] Z. Akyuz, S. Halici, Some identities deriving from the nth power of a special matrix, Adv. Difference Equ., (2012(1)), 1-6.
  • [6] C. K. Cook, Some sums related to sums of Oresme numbers, In Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications, (2004), 87-99.
  • [7] James Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2x2 matrix, Integers, 4 (2004), A19.
  • [8] N. Oresme, Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961).
  • [9] A. F. Horadam, Oresme Numbers, Fibonacci Quart., 12(3) (1974), 267- 271.
  • [10] G. Y. Senturk, N. Gurses, S. Yuce, A new look on Oresme numbers: dual-generalized complex component extension, In Conference Proceeding Science and Technology, 1(1) (2018), 254-265.
  • [11] G. Cerda Morales, Oresme polynomials and their derivatives, arXiv preprint arXiv:1904.01165, (2019).
  • [12] S. Halici, E. Sayin, Z. B. Gur, k- Oresme numbers and k- Oresme numbers with negative indices, ICMASE (2022), 211-223.
  • [13] S. Halici, E. Sayin, On some k􀀀 Oresme hybrid numbers, Util. Math., 120, (2023), 1-11.
  • [14] S. Halici, Z. B. Gur, E. Sayin, k- Oresme polynomials and their derivatives, ICMASE, (2022), 201-210.
  • [15] S. Halici, Z. B. Gur, On some derivatives of k- Oresme polynomials, Bulletin of IMVI, 13(1) (2023), 41-50.
  • [16] Y. Soykan, A study on generalized p- Oresme numbers, Asian Journal of Advanced Research and Reports, 15(7) (2021), 1-25.
There are 16 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Articles
Authors

Elifcan Sayın 0000-0001-5602-7681

Serpil Halıcı 0000-0002-8071-0437

Early Pub Date June 5, 2024
Publication Date
Submission Date February 28, 2024
Acceptance Date April 28, 2024
Published in Issue Year 2024 Volume: 7 Issue: 2

Cite

APA Sayın, E., & Halıcı, S. (2024). On Some k-Oresme Polynomials with Negative Indices. Communications in Advanced Mathematical Sciences, 7(2), 71-79. https://doi.org/10.33434/cams.1444712
AMA Sayın E, Halıcı S. On Some k-Oresme Polynomials with Negative Indices. Communications in Advanced Mathematical Sciences. June 2024;7(2):71-79. doi:10.33434/cams.1444712
Chicago Sayın, Elifcan, and Serpil Halıcı. “On Some K-Oresme Polynomials With Negative Indices”. Communications in Advanced Mathematical Sciences 7, no. 2 (June 2024): 71-79. https://doi.org/10.33434/cams.1444712.
EndNote Sayın E, Halıcı S (June 1, 2024) On Some k-Oresme Polynomials with Negative Indices. Communications in Advanced Mathematical Sciences 7 2 71–79.
IEEE E. Sayın and S. Halıcı, “On Some k-Oresme Polynomials with Negative Indices”, Communications in Advanced Mathematical Sciences, vol. 7, no. 2, pp. 71–79, 2024, doi: 10.33434/cams.1444712.
ISNAD Sayın, Elifcan - Halıcı, Serpil. “On Some K-Oresme Polynomials With Negative Indices”. Communications in Advanced Mathematical Sciences 7/2 (June 2024), 71-79. https://doi.org/10.33434/cams.1444712.
JAMA Sayın E, Halıcı S. On Some k-Oresme Polynomials with Negative Indices. Communications in Advanced Mathematical Sciences. 2024;7:71–79.
MLA Sayın, Elifcan and Serpil Halıcı. “On Some K-Oresme Polynomials With Negative Indices”. Communications in Advanced Mathematical Sciences, vol. 7, no. 2, 2024, pp. 71-79, doi:10.33434/cams.1444712.
Vancouver Sayın E, Halıcı S. On Some k-Oresme Polynomials with Negative Indices. Communications in Advanced Mathematical Sciences. 2024;7(2):71-9.

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