On Lucas-balancing-like Polynomials
Resumen
In this work, we defined the Lucas–balancing-like polynomials and established their connection to
the Chebyshev polynomials. We also derived metallic ratios by computing the limits of successive polynomial
terms. Subsequently, we examined the structural relationship between the balancing-like polynomials and the
Lucas–balancing-like polynomials introduced in this article and obtained various algebraic identities.
Key Words: Balancing polynomials, Fibonacci sequence, Chebyshev polynomials.
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Citas
1. Behera, A., Panda, G.K.,On the square roots of triangular numbers, Fibonacci Quarterly, 37(2), 98-105, (1999).
2. Dutta, U.K., Ray, P.K., Euler-zagier multiple l-functions involving balancing-likepolynomıals associated to dirichlet
characters, Palestine Journal of Mathematics, 11, 274-289, (2022).
3. Frontczak, R., On balancing polynomials, Applied Mathematical Science, 13, 57-66, (2019).
4. Koshy, T., Fibonacci and Lucas numbers with applications, Willey, Canada, (2001).
5. Mason, J.C, Hamdscomb, D.C., Chebyshev polynomials, Chapman/CRC, Florida, (2003).
6. Ozkan, E., Akku¸s, H., ¨ Copper ratio obtained by generalizing the Fibonaccisequence, AIP Advances, 14, (2024).
7. Ozkan, E., Tekeo˘glu Akkaya, B., ¨ On the properties of balancing-like polynomials.
8. OZkan, E., Tekeo˘glu Akkaya, B., ¨ On k-balancing-like-sequences and k-Lucas-balancing-like-sequences.
9. Panda, G.K., Some fascinating properties of balancing numbers, Fibonacci Numbers and Their Applications, 10, (2006).
10. Panda, G.K., Rout, S.S., A class of recurrent sequences exhibiting some exciting properties of balancing numbers,
International Journal of Mathematical,Computational, Physical, Electrical and Computer Engineering, 6, 4-6, (2012).
11. Panda, A.K., Some variants of the balancing sequence, , Thesis(PhD), Department of mathematics national ınstitute
of technology, (2016).
12. Rout, S.S., Some generalizations and properties of balancing numbers, Thesis(PhD), Department of mathematics national ınstitute of technology, (2015).
13. Ray, P.K., New identities for the common factors of balancing and Lucas-balancing numbers, International Journal of
Pure and Applied Mathematics, 85, 487-494 , (2013).
14. Ray, P.K., Balancing and cobalancing numbers, Thesis(PhD), Department of mathematics national ınstitute of technology, (2009).
15. Ta¸s¸cı, D., Gaussian balancing numbers and Gaussian Lucas balancing numbers, Journal of Science and Arts, 3, 661-666,
(2018).
16. Tekeo˘glu, B., KAradeniz G¨ozeri, G., Some properties of balancing-like sequences, Thesis(Master), Istanbul University,
(2024).
17. Uysal, M., Ozkan, E., Shannon, A.G., ¨ On dual bicomplex balancing and Lucas-balancing numbers, Journal of Science
and Arts, 23, 925-938, (2023).
18. Vajda, S., Fibonacci & Lucas numbers, and the Golden section, Ellıs Horwood Limited, West Sussex, (1989).
2. Dutta, U.K., Ray, P.K., Euler-zagier multiple l-functions involving balancing-likepolynomıals associated to dirichlet
characters, Palestine Journal of Mathematics, 11, 274-289, (2022).
3. Frontczak, R., On balancing polynomials, Applied Mathematical Science, 13, 57-66, (2019).
4. Koshy, T., Fibonacci and Lucas numbers with applications, Willey, Canada, (2001).
5. Mason, J.C, Hamdscomb, D.C., Chebyshev polynomials, Chapman/CRC, Florida, (2003).
6. Ozkan, E., Akku¸s, H., ¨ Copper ratio obtained by generalizing the Fibonaccisequence, AIP Advances, 14, (2024).
7. Ozkan, E., Tekeo˘glu Akkaya, B., ¨ On the properties of balancing-like polynomials.
8. OZkan, E., Tekeo˘glu Akkaya, B., ¨ On k-balancing-like-sequences and k-Lucas-balancing-like-sequences.
9. Panda, G.K., Some fascinating properties of balancing numbers, Fibonacci Numbers and Their Applications, 10, (2006).
10. Panda, G.K., Rout, S.S., A class of recurrent sequences exhibiting some exciting properties of balancing numbers,
International Journal of Mathematical,Computational, Physical, Electrical and Computer Engineering, 6, 4-6, (2012).
11. Panda, A.K., Some variants of the balancing sequence, , Thesis(PhD), Department of mathematics national ınstitute
of technology, (2016).
12. Rout, S.S., Some generalizations and properties of balancing numbers, Thesis(PhD), Department of mathematics national ınstitute of technology, (2015).
13. Ray, P.K., New identities for the common factors of balancing and Lucas-balancing numbers, International Journal of
Pure and Applied Mathematics, 85, 487-494 , (2013).
14. Ray, P.K., Balancing and cobalancing numbers, Thesis(PhD), Department of mathematics national ınstitute of technology, (2009).
15. Ta¸s¸cı, D., Gaussian balancing numbers and Gaussian Lucas balancing numbers, Journal of Science and Arts, 3, 661-666,
(2018).
16. Tekeo˘glu, B., KAradeniz G¨ozeri, G., Some properties of balancing-like sequences, Thesis(Master), Istanbul University,
(2024).
17. Uysal, M., Ozkan, E., Shannon, A.G., ¨ On dual bicomplex balancing and Lucas-balancing numbers, Journal of Science
and Arts, 23, 925-938, (2023).
18. Vajda, S., Fibonacci & Lucas numbers, and the Golden section, Ellıs Horwood Limited, West Sussex, (1989).
Publicado
2026-02-16
Sección
Special Issue: Advances in Mathematical Sciences
Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
