Diagonal Function of k-Lucas Polynomials

Yogesh Kumar Gupta^1, , V. H. Badshah¹, Mamta Singh² and Kiran Sisodiya¹

¹School of Studies in Mathematics, Vikram University Ujjain, (M. P.) India

²Department of Mathematical Science and Computer applications, Bundelkhand University, Jhansi (U. P.) India

Cite this paper:
Yogesh Kumar Gupta, V. H. Badshah, Mamta Singh and Kiran Sisodiya. Diagonal Function of k-Lucas Polynomials. Turkish Journal of Analysis and Number Theory. 2015; 3(2):49-52. doi: 10.12691/tjant-3-2-3

Abstract

The Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, Diagonal function of k-Lucas Polynomials is introduced and defined by G_n+1(x)=kxG_n(x)+G_n-2,(x), n≥1. with G₀(x)=2. and G₁(x)=1 Some Lucas Polynomials, rising & descending diagonal function and generating matrix established and derived by standard methods.

Keywords:
Lucas Polynomials rising diagonal function descending diagonal function and generating matrix

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	A.F Hordam, Diagonal Function, the Fibonacci Quarterly, Vol. 16, 19-36.
[2]	Alexandra Lupas Guide of Fibonacci and Lucas polynomials, Octagon Mathematics Magazine Vo. 17, No.1 (1999), 2-12.
[3]	B.S.Porov, A note on the sum of Fibonacci and Lucas polynomials, The Fill Quarterly 1970, 428-438.
[4]	D.V. Jaiswal, “Some Metric Properties of a Generalized Fibonacci Sequence’’, Labdev Journal of Science and technology, India vol.11-A, No.1, 1973, 1-3.
[5]	Jr. V.E. Hoggatt, Fibonacci and Lucas Numbers, Houshton Mifflin Company, Borton, 1965.
[6]	Koshy, T. Fibonacci and Lucas number with application, Wiley, 2001.
[7]	M. Catalan, An Identity for Lucas Polynomials, Fibonacci Quarterly Vol 43, No.1 2005.
[8]	Singh, B., S. Teeth, and Harne Diagonal Function of Fibonacci Polynomials, chh. J. Sci. Tech 2005, 97-102.
[9]	Vajda, S. Fibonacci and Lucas numbers and the golden section, Ellis Horwood Limited, Chi Chester, England, 1989.
[10]	Vorobyou, N.N., The Fibonacci number, D.C. health company, Boston, 1963.