Composition Identities of Chebyshev Polynomials, via 2 × 2 Matrix Powers

Symmetry

Primo Brandi¹  PaoloEmilio Ricci² 

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia, Italy;International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;

关键词: Chebyshev polynomials;    matrix powers;    composition identities;   

DOI  :  10.3390/sym12050746

来源: DOAJ

【 摘 要 】

Starting from a representation formula for $2\times 2$ non-singular complex matrices in terms of 2nd kind Chebyshev polynomials, a link is observed between the 1st kind Chebyshev polinomials and traces of matrix powers. Then, the standard composition of matrix powers is used in order to derive composition identities of 2nd and 1st kind Chebyshev polynomials. Before concluding the paper, the possibility to extend this procedure to the multivariate Chebyshev and Lucas polynomials is touched on.

【 授权许可】

Unknown