TY - JOUR T1 - On Some k-Oresme Polynomials with Negative Indices AU - Sayın, Elifcan AU - Halıcı, Serpil PY - 2024 DA - June Y2 - 2024 DO - 10.33434/cams.1444712 JF - Communications in Advanced Mathematical Sciences PB - Emrah Evren KARA WT - DergiPark SN - 2651-4001 SP - 71 EP - 79 VL - 7 IS - 2 LA - en AB - 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. KW - Matrices KW - Recurrences KW - Special sequences and polynomials CR - [1] A. F. Horadam, Special properties of the sequenceWn(a;b; p;q) , Fibonacci Quart., 5(5) (1967), 424-434. CR - [2] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, 3(3) (1965), Fibonacci Quart., 161-176. CR - [3] A. F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly, 68(5) (1961), 455-459. CR - [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. CR - [5] Z. Akyuz, S. Halici, Some identities deriving from the nth power of a special matrix, Adv. Difference Equ., (2012(1)), 1-6. CR - [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. CR - [7] James Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2x2 matrix, Integers, 4 (2004), A19. CR - [8] N. Oresme, Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961). CR - [9] A. F. Horadam, Oresme Numbers, Fibonacci Quart., 12(3) (1974), 267- 271. CR - [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. CR - [11] G. Cerda Morales, Oresme polynomials and their derivatives, arXiv preprint arXiv:1904.01165, (2019). CR - [12] S. Halici, E. Sayin, Z. B. Gur, k- Oresme numbers and k- Oresme numbers with negative indices, ICMASE (2022), 211-223. CR - [13] S. Halici, E. Sayin, On some k􀀀 Oresme hybrid numbers, Util. Math., 120, (2023), 1-11. CR - [14] S. Halici, Z. B. Gur, E. Sayin, k- Oresme polynomials and their derivatives, ICMASE, (2022), 201-210. CR - [15] S. Halici, Z. B. Gur, On some derivatives of k- Oresme polynomials, Bulletin of IMVI, 13(1) (2023), 41-50. CR - [16] Y. Soykan, A study on generalized p- Oresme numbers, Asian Journal of Advanced Research and Reports, 15(7) (2021), 1-25. UR - https://doi.org/10.33434/cams.1444712 L1 - https://dergipark.org.tr/en/download/article-file/3762073 ER -