Details:
Title  Decomposition of perturbed Chebyshev polynomials  Author(s)  Stephan Thomasse  Type  Article in Journal  Abstract  We characterize polynomial decomposition f n = r ∘ q with r , q ∈ C [ x ] of perturbed Chebyshev polynomials defined by the recurrence f 0 ( x ) = b , f 1 ( x ) = x  c , f n + 1 ( x ) = ( x  d ) f n ( x )  af n  1 ( x ) , n ⩾ 1 , where a , b , c , d ∈ R and a > 0 . These polynomials generalize the Chebyshev polynomials, which are obtained by setting a = 1 4 , c = d = 0 and b ∈ 1 , 2 . At the core of the method, two algorithms for polynomial decomposition are provided, which allow to restrict the investigation to the resolution of six systems of polynomial equations in three variables. The final task is then carried out by the successful computation of reduced Gröbner bases with Maple 10. Some additional data for the calculations are available on the author  Keywords  Corecursive and codilated orthogonal polynomials, Chebyshev polynomials, Polynomial decomposition, Gröbner bases  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S037704270700132X 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  214  Number  2  Pages  356  370  Year  2008  Edition  0  Translation 
No  Refereed 
No 
