Chebyshev polynomials and the minimal polynomial of cos(2π/n) (II)

Abstract

We present methods to write T_n(x), Chebyshev polynomials of the first kind, as a product of minimal polynomials of cos(2π/m) over integers, Ψ_m(x), and to write Ψ_m(x) as ratios of expressions in T_n(x). We also prove the relation Ψ_m(T_n(x)) = Ψ_n(T_m(x)) for m, n having the same prime divisors and use it to express Ψ_m(x) as a linear combination of T_n(x) for certain values of m.

Subject Classification: (2010):

• Primary 11C08

Keywords:

• Chebyshev polynomial
• Minimal polynomial
• Cosine
• 2π/n