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
References
- [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.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Nusret Karaaslan
*
Türkiye
Publication Date
June 30, 2019
Submission Date
January 11, 2019
Acceptance Date
February 13, 2019
Published in Issue
Year 1970 Volume: 3 Number: 1
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