Araştırma Makalesi
BibTex RIS Kaynak Göster

d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations

Yıl 2022, Cilt: 14 Sayı: 2, 262 - 270, 30.12.2022
https://doi.org/10.47000/tjmcs.1007382

Öz

We define a new generalization of Gaussian Pell-Lucas polynomials. We call it $d-$Gaussian Pell-Lucas polynomials. Then we present the generating function and Binet formula for the polynomials. We give a matrix representation of $d-$Gaussian Pell-Lucas polynomials. Using the Riordan method, we obtain the factorizations of Pascal matrix involving the polynomials.

Kaynakça

  • Çelik, S., Durukan, İ.,Özkan, E., New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers, Chaos, Solitons and Fractals, 150(2021), 111173.
  • Halıcı, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Journal of Science and Tecnology, 6(1)(2016), 8–18.
  • Halıcı, S., Öz, S., On Gaussian Pell polynomials and their some properties, Palestine Journal of Mathematics, 7(1)(2018), 251–256.
  • Hoggatt, V.E., Fibonacci and Lucas Numbers, Houghton Mifflin, Boston, 1969.
  • Horadam, A.F., Mahon, J.M., Pell and Pell-Lucas polynomials, The Fibonacci Quarterly, 23(1)(1985), 7-20.
  • Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • Mikkawy, M., Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation,215(2010), 4456–4461.
  • Özkan, E., Göçer, A., Altun, İ., A new sequence realizing Lucas numbers, and the Lucas bound, Electronic Journal of Mathematical Analysis and Applications, 5(1)(2017), 148–154.
  • Özkan, E., Tastan, M., On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications, Communications in Algebra, 48(3)(2020), 952–960.
  • Özkan, E., Tastan, M., A new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers and their polynomials, Journal of Science and Arts, 4(53)(2020), 893–908.
  • Özkan, E., Tastan, M., On Gauss k-Fibonacci polynomials, Electronic Journal of Mathematical Analysis and Applications, 9(1)(2021), 124–130.
  • Özkan, E., Kuloğlu, B., On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials, Asian-European Journal of Mathematics, 14(2021), 2150100.
  • Özkan, E., Kuloğlu, B., Peters, J., K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity, Chaos, Solitons and Fractals, 153(2021).
  • Özkan, E., Yılmaz, N.Ş.,Włoch, A., On F3(k,n)-numbers of the Fibonacci type, Bolet´ın de la SociedadMatema´ticaMexicana , 27(2021), 1-18.
  • Sadaoui, B., Krelifa, A., d- Fibonacci and d- Lucas polynomials, Journal of Mathematical Modeling, 9(3)(2021),1–12.
  • Shannon, A.G.,Fibonacci analogs of the classical polynomials, Mathematics Magazine,48(3)(1975), 123–130.
  • Shapiro, L.W., Getu, S., Woan, W.J., Woodson, L.C., The Riordan group, Discrete Applied Mathematics, 34(1-3)(1991), 229–239.
  • Sloane, N.J.A., A Handbook of Integer Sequences, Academic Press, New York, 1973.
  • Yagmur, T., Gaussian Pell-Lucas polynomials, Communications in Mathematics and Applications, 10(4)(2019), 673–679.
Yıl 2022, Cilt: 14 Sayı: 2, 262 - 270, 30.12.2022
https://doi.org/10.47000/tjmcs.1007382

Öz

Kaynakça

  • Çelik, S., Durukan, İ.,Özkan, E., New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers, Chaos, Solitons and Fractals, 150(2021), 111173.
  • Halıcı, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Journal of Science and Tecnology, 6(1)(2016), 8–18.
  • Halıcı, S., Öz, S., On Gaussian Pell polynomials and their some properties, Palestine Journal of Mathematics, 7(1)(2018), 251–256.
  • Hoggatt, V.E., Fibonacci and Lucas Numbers, Houghton Mifflin, Boston, 1969.
  • Horadam, A.F., Mahon, J.M., Pell and Pell-Lucas polynomials, The Fibonacci Quarterly, 23(1)(1985), 7-20.
  • Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • Mikkawy, M., Sogabe, T., A new family of k-Fibonacci numbers, Applied Mathematics and Computation,215(2010), 4456–4461.
  • Özkan, E., Göçer, A., Altun, İ., A new sequence realizing Lucas numbers, and the Lucas bound, Electronic Journal of Mathematical Analysis and Applications, 5(1)(2017), 148–154.
  • Özkan, E., Tastan, M., On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications, Communications in Algebra, 48(3)(2020), 952–960.
  • Özkan, E., Tastan, M., A new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers and their polynomials, Journal of Science and Arts, 4(53)(2020), 893–908.
  • Özkan, E., Tastan, M., On Gauss k-Fibonacci polynomials, Electronic Journal of Mathematical Analysis and Applications, 9(1)(2021), 124–130.
  • Özkan, E., Kuloğlu, B., On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials, Asian-European Journal of Mathematics, 14(2021), 2150100.
  • Özkan, E., Kuloğlu, B., Peters, J., K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity, Chaos, Solitons and Fractals, 153(2021).
  • Özkan, E., Yılmaz, N.Ş.,Włoch, A., On F3(k,n)-numbers of the Fibonacci type, Bolet´ın de la SociedadMatema´ticaMexicana , 27(2021), 1-18.
  • Sadaoui, B., Krelifa, A., d- Fibonacci and d- Lucas polynomials, Journal of Mathematical Modeling, 9(3)(2021),1–12.
  • Shannon, A.G.,Fibonacci analogs of the classical polynomials, Mathematics Magazine,48(3)(1975), 123–130.
  • Shapiro, L.W., Getu, S., Woan, W.J., Woodson, L.C., The Riordan group, Discrete Applied Mathematics, 34(1-3)(1991), 229–239.
  • Sloane, N.J.A., A Handbook of Integer Sequences, Academic Press, New York, 1973.
  • Yagmur, T., Gaussian Pell-Lucas polynomials, Communications in Mathematics and Applications, 10(4)(2019), 673–679.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Engin Özkan 0000-0002-4188-7248

Mine Uysal 0000-0002-2362-3097

Erken Görünüm Tarihi 23 Aralık 2022
Yayımlanma Tarihi 30 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 14 Sayı: 2

Kaynak Göster

APA Özkan, E., & Uysal, M. (2022). d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations. Turkish Journal of Mathematics and Computer Science, 14(2), 262-270. https://doi.org/10.47000/tjmcs.1007382
AMA Özkan E, Uysal M. d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations. TJMCS. Aralık 2022;14(2):262-270. doi:10.47000/tjmcs.1007382
Chicago Özkan, Engin, ve Mine Uysal. “D-Gaussian Pell-Lucas Polynomials and Their Matrix Representations”. Turkish Journal of Mathematics and Computer Science 14, sy. 2 (Aralık 2022): 262-70. https://doi.org/10.47000/tjmcs.1007382.
EndNote Özkan E, Uysal M (01 Aralık 2022) d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations. Turkish Journal of Mathematics and Computer Science 14 2 262–270.
IEEE E. Özkan ve M. Uysal, “d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations”, TJMCS, c. 14, sy. 2, ss. 262–270, 2022, doi: 10.47000/tjmcs.1007382.
ISNAD Özkan, Engin - Uysal, Mine. “D-Gaussian Pell-Lucas Polynomials and Their Matrix Representations”. Turkish Journal of Mathematics and Computer Science 14/2 (Aralık 2022), 262-270. https://doi.org/10.47000/tjmcs.1007382.
JAMA Özkan E, Uysal M. d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations. TJMCS. 2022;14:262–270.
MLA Özkan, Engin ve Mine Uysal. “D-Gaussian Pell-Lucas Polynomials and Their Matrix Representations”. Turkish Journal of Mathematics and Computer Science, c. 14, sy. 2, 2022, ss. 262-70, doi:10.47000/tjmcs.1007382.
Vancouver Özkan E, Uysal M. d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations. TJMCS. 2022;14(2):262-70.