A Note on Modified Pell Polynomials
Abstract
In this paper, we study the modified Pell polynomials. We first give the proof of the generating function of these polynomials. We then give the proof of the Binet formula for the modified Pell polynomials, which gives the th modified Pell polynomial. We also obtain some summation formula for these polynomials. In addition, we investigate some well-known identities including Catalan, Cassini, d’Ocagne and Gelin-Cesaro identities involving the modified Pell polynomials.
Keywords
Kaynakça
- [1] V.E. Hoggatt Jr., Fibonacci and Lucas Numbers (Houghton Mifflin, Boston, 1969).
- [2] T. Koshy, Fibonacci and Lucas Numbers with Applications (Wiley-Interscience, New York, 2001) pp. 51-131.
- [3] S. Vajda, Fibonacci & Lucas Numbers and The Golden Section: Theory and Applications (John Wiley and Sons, New York, 1989) pp. 9-61.
- [4] T. Koshy, Pell and Pell-Lucas Numbers with Applications (Springer, New York, 2014).
- [5] A.F. Horadam, Applications of modified Pell numbers to representations. Ulam Quarterly, 3(1) (1994) 34-53.
- [6] R. Melham, Sums involving Fibonacci and Pell numbers. Portugaliae Mathematica, 56(3) (1999) 309-317.
- [7] S. Halıcı and A. Daşdemir, On some relationships among Pell, Pell-Lucas and modified Pell sequences. Sakarya University Journal of Science, 14(2) (2010) 141-145.
- [8] Y. Yuan and W. Zhang, Some identities involving the Fibonacci polynomials.The Fibonacci Quarterly, 40 (2002) 314-318.
Ayrıntılar
Birincil Dil
İngilizce
Konular
-
Bölüm
Araştırma Makalesi
Yazarlar
Nusret Karaaslan
*
Türkiye
Yayımlanma Tarihi
30 Haziran 2019
Gönderilme Tarihi
11 Ocak 2019
Kabul Tarihi
13 Şubat 2019
Yayımlandığı Sayı
Yıl 1970 Cilt: 3 Sayı: 1
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