SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 2

(p; q)-FIBONACCI AND (p; q)-LUCAS SUMS BY THE DERIVATIVES OF SOME POLYNOMIALS

B. DEMİRTÜRK BİTİM
N. TOPAL
Pages
1733–1741
Publication Date
2019-08-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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
📊
Key Findings & Data: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
💡
Conclusion & Impact: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
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci polynomial · Lucas polynomial · sum of products

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

🔖

Cite This Article

BİTİM, B. D., 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, Cilt: 68 - Sayı: 2, 1733–1741. https://ajindex.com/articles/746946

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Amini, A.R., Fibonacci numbers from a long division formula, Mathematical Spectrum, 40 (2008), 59-61.
  2. Belbachir, H. and Bencherif, F., Sums of products of generalized Fibonacci and Lucas numbers, arXiv: 0708.2347v1, 17.08.2007.
  3. 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.
  4. Chong, C. Y., Cheah, C. L. and Ho, C. K., Some identities of generalized Fibonacci sequence, AIP Conf. Proc., 1605 (2014), 661-665.
  5. Horadam, A. F., Basic properties of certain generalized sequences of numbers, Fibonacci Quart., 3(5), (1965), 161-176.
  6. Koshy, T., Fibonacci and Lucas numbers with applications, Wiley and Sons, Canada, 2001.
  7. Long, C. T., Discovering Fibonacci identities, Fibonacci Quart., 24(2), (1986), 160-167.
  8. Lucas, E., Théorie des fonctions numériques simplement périodiques, Amer. J. Math., 1 (1878), 184-240.
  9. Melham, R. S., On sums of powers of terms in a linear recurrence, Port. Math., 56(4), (1999), 501-508.
  10. Shannon, A. G. and Horadam, A. F., Special recurrence relations associated with the sequence {w_{n}(a,b;p,q)}, Fibonacci Quart., 17(4), (1979), 294-299.
  11. Vajda, S., Fibonacci and Lucas numbers and the golden section, Ellis Horwood Ltd. Publ., England, 1989.