AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS

Authors

  • Luu Ba Thang Faculty of Mathematics and Informatics, Hanoi National University of Education, Hanoi city, Vietnam
  • Nguyen Duc Sang Faculty of Mathematics and Informatics, Hanoi National University of Education, Hanoi city, Vietnam

DOI:

https://doi.org/10.18173/2354-1059.2025-0002

Keywords:

Pell sequence, Pell-Lucas sequences, integral representations

Abstract

We report on an integral representation for the Pell sequence, Pell-Lucas sequence, Balancing sequence and Lucas-Balancing sequence. This integral representation  is based on the generating function  and  the Binet-like formulas of the aforementioned sequences. Many other integral representations of these numbers can be found by applying the other known relations between them.

References

[1] Glasser ML & Zhou Y (2015) An integral representation for the Fibonacci numbers and their generalization. Fibonacci Quart 53:313–318

[2] Stewart SM (2023) A simple integral representation of the Fibonacci numbers. The Mathematical Gazette 107(568):120–123

[3] Koshy T (2010) Pell and Pell–Lucas numbers with applications. Springer-Verlag, New York

[4] Koshy T (2019) Fibonacci and Lucas numbers with applications, Vol 2. John Wiley and Sons

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Published

31-03-2025

Issue

Volume 70, Issue 1, 2025: Natural Sciences

Section

Articles

How to Cite

Luu Ba Thang, & Nguyen Duc Sang. (2025). AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS. Journal of Science Natural Science, 70(1), 15-21. https://doi.org/10.18173/2354-1059.2025-0002