Turkish Journal of Analysis and Number Theory. 2015, 3(2), 49-52
DOI: 10.12691/tjant-3-2-3
Open AccessArticle
Yogesh Kumar Gupta1, , 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
Pub. Date: May 04, 2015
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 Gn+1(x)=kxGn(x)+Gn-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
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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. |
|