A “Hard to Die” Series Expansion and Lucas Polynomials of the Second Kind
Affiliation(s)
1 Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italia. 2 International Telematic University UNINETTUNO, Roma, Italia.
1 Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italia. 2 International Telematic University UNINETTUNO, Roma, Italia.
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.
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
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.
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.
[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.