A Note on Modified Pell Polynomials

Nusret Karaaslan

doi:10.29002/asujse.511850

Research Article

Year 2019, , 1 - 7, 30.06.2019

Nusret Karaaslan

https://doi.org/10.29002/asujse.511850

Cited By: 2

Abstract

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.
[9] B.G.S. Doman and J.K. Williams, Fibonacci and Lucas polynomials. Mathematical Proceedings of the Cambridge Philosophical Society, 90(3) (1981) 385-387.
[10] A. Lupas, A guide of Fibonacci and Lucas polynomial. Octagon Mathematics Magazine, 7(1) (1999) 2-12.
[11] W.A. Webb and E.A. Parberry, Divisibility properties of Fibonacci polynomials. The Fibonacci Quarterly, 7(5) (1969) 457-463.
[12] A.F. Horadam and Bro. J.M. Mahon, Pell and Pell-Lucas polynomials. The Fibonacci Quarterly, 23(1) (1985) 7-20.
[13] T. Horzum and E. G. Kocer, On Some Properties of Horadam Polynomials, International Mathematical Forum, 4(25) (2009) 1243-1252.

A Note on Modified Pell Polynomials

Year 2019, , 1 - 7, 30.06.2019

Nusret Karaaslan

https://doi.org/10.29002/asujse.511850

Cited By: 2

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

Modified Pell sequence, Modified Pell polynomial sequence

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.
[9] B.G.S. Doman and J.K. Williams, Fibonacci and Lucas polynomials. Mathematical Proceedings of the Cambridge Philosophical Society, 90(3) (1981) 385-387.
[10] A. Lupas, A guide of Fibonacci and Lucas polynomial. Octagon Mathematics Magazine, 7(1) (1999) 2-12.
[11] W.A. Webb and E.A. Parberry, Divisibility properties of Fibonacci polynomials. The Fibonacci Quarterly, 7(5) (1969) 457-463.
[12] A.F. Horadam and Bro. J.M. Mahon, Pell and Pell-Lucas polynomials. The Fibonacci Quarterly, 23(1) (1985) 7-20.
[13] T. Horzum and E. G. Kocer, On Some Properties of Horadam Polynomials, International Mathematical Forum, 4(25) (2009) 1243-1252.

There are 13 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Nusret Karaaslan
Publication Date	June 30, 2019
Submission Date	January 11, 2019
Acceptance Date	February 13, 2019
Published in Issue	Year 2019

Cite

APA	Karaaslan, N. (2019). A Note on Modified Pell Polynomials. Aksaray University Journal of Science and Engineering, 3(1), 1-7. https://doi.org/10.29002/asujse.511850