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 AM  Vol.6 No.8 , July 2015
A “Hard to Die” Series Expansion and Lucas Polynomials of the Second Kind
Pierpaolo Natalini1*, Paolo E. Ricci2
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Abstract: We show how to use the Lucas polynomials of the second kind in the solution of a homogeneous linear differential system with constant coefficients, avoiding the Jordan canonical form for the relevant matrix.
Keywords: Homogeneous Linear Differential Systems with Constant Coefficients, Exponential Matrix, Lucas Polynomials of the Second Kind
Cite this paper: Natalini, P. and Ricci, P. (2015) A “Hard to Die” Series Expansion and Lucas Polynomials of the Second Kind. Applied Mathematics, 6, 1235-1240. doi: 10.4236/am.2015.68116.
References

[1]   Gantmacher, F.R. (1960) Matrix Theory. Chelsea Pub. Co., New York.

[2]   Hirsch, M.W., Smale, S. and Devaney, R.L. (2003) Differential Equations, Dynamical Systems & an Introduction to Chaos. Academic Press, Elsevier, London.

[3]   Raghavacharyulu, I.V.V. and Tekumalla, A.R. (1972) Solution of the Difference Equations of Generalized Lucas Polynomials. Journal of Mathematical Physics, 13, 321-324.
http://dx.doi.org/10.1063/1.1665978

[4]   Bruschi, M. and Ricci, P.E. (1982) An Explicit Formula for f(A) and the Generating Function of the Generalized Lucas Polynomials. SIAM Journal on Mathematical Analysis, 13, 162-165.
http://dx.doi.org/10.1137/0513012

[5]   Bruschi, M. and Ricci, P.E. (1980) I polinomi di Lucas e di Tchebycheff in più variabili. Rendiconti di Matematica e delle sue Applicazioni, 13, 507-530.

[6]   Ricci, P.E. (1976) Sulle potenze di una matrice. Rendiconti di Matematica e delle sue Applicazioni, 9, 179-194.

[7]   Lucas, é. (1891) Théorie des Nombres. Gauthier-Villars, Paris.

 
 
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