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Full-Text Articles in Mathematics
Combinatorial Trigonometry With Chebyshev Polynomials, Arthur T. Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck
Combinatorial Trigonometry With Chebyshev Polynomials, Arthur T. Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck
All HMC Faculty Publications and Research
We provide a combinatorial proof of the trigonometric identity cos(nθ) = Tncos(θ),
where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.
Combinatorially Composing Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07
Combinatorially Composing Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07
All HMC Faculty Publications and Research
We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n ≥ 0, Tm(Tn(x)) = Tmn(x) and Um-1 (Tn(x))Un-1(x) = Umn-1(x).