EN
(p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS
Abstract
The main purpose of this paper is to survey several sum formulae of (p,q)-Fibonacci number U_{n} and (p,q)-Lucas number V_{n} by using the first and the second derivatives of the equations
xⁿ=(x²-px+q)(∑U_{j}x^{n-1-j})+U_{n}x-qU_{n-1}
and
2xⁿ⁺¹-pxⁿ=(x²-px+q)(∑V_{j}x^{n-1-j})+V_{n}x-qV_{n-1}.
Keywords
References
- Amini, A.R., Fibonacci numbers from a long division formula, Mathematical Spectrum, 40 (2008), 59-61.
- Belbachir, H. and Bencherif, F., Sums of products of generalized Fibonacci and Lucas numbers, arXiv: 0708.2347v1, 17.08.2007.
- Benjamin, A. T. and Quinn, J. J., Proofs that really count, the art of combinatorial proofs, Mathematical Association of America, Providence, RI, 2003.
- Čerin, Z., Sums of products of generalized Fibonacci and Lucas numbers, Demonstratio Math., 42(2), (2009), 247-258.
- Čerin, Z., Some alternating sums of Lucas numbers, Cent. Eur. J. Math., 3(1), (2015), 1-13.
- Čerin, Z., Bitim, B. D. and Keskin, R., Sum formulae of generalized Fibonacci and Lucas numbers, Honam Math. J., 40(1), (2018), 199-210.
- Chong, C. Y., Cheah, C. L. and Ho, C. K., Some identities of generalized Fibonacci sequence, AIP Conf. Proc., 1605 (2014), 661-665 .
- Horadam, A. F., Basic properties of certain generalized sequences of numbers, Fibonacci Quart., 3(5), (1965), 161-176.
Details
Primary Language
English
Subjects
Applied Mathematics
Journal Section
Research Article
Publication Date
August 1, 2019
Submission Date
October 31, 2017
Acceptance Date
February 16, 2019
Published in Issue
Year 2019 Volume: 68 Number: 2
APA
Demirtürk Bitim, B., & Topal, N. (2019). (p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1733-1741. https://doi.org/10.31801/cfsuasmas.551883
AMA
1.Demirtürk Bitim B, Topal N. (p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1733-1741. doi:10.31801/cfsuasmas.551883
Chicago
Demirtürk Bitim, B., and N. Topal. 2019. “(p; Q)-FIBONACCI AND (p; Q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2): 1733-41. https://doi.org/10.31801/cfsuasmas.551883.
EndNote
Demirtürk Bitim B, Topal N (August 1, 2019) (p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1733–1741.
IEEE
[1]B. Demirtürk Bitim and N. Topal, “(p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1733–1741, Aug. 2019, doi: 10.31801/cfsuasmas.551883.
ISNAD
Demirtürk Bitim, B. - Topal, N. “(p; Q)-FIBONACCI AND (p; Q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 1, 2019): 1733-1741. https://doi.org/10.31801/cfsuasmas.551883.
JAMA
1.Demirtürk Bitim B, Topal N. (p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1733–1741.
MLA
Demirtürk Bitim, B., and N. Topal. “(p; Q)-FIBONACCI AND (p; Q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, Aug. 2019, pp. 1733-41, doi:10.31801/cfsuasmas.551883.
Vancouver
1.B. Demirtürk Bitim, N. Topal. (p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Aug. 1;68(2):1733-41. doi:10.31801/cfsuasmas.551883
Cited By
On identities associated with generalized Fibonacci and Tribonacci numbers using matrices
Journal of Difference Equations and Applications
https://doi.org/10.1080/10236198.2025.2589263