Chebyshev polynomials of the first kind T_n are defined by the trigonometric identity T_n(cos θ) = cos(n θ), with closed forms T_0 = 1, T_1 = x, T_{n+1} = 2x T_n − T_{n-1}. Two defining properties: (i) orthogonality on [−1, 1] with weight…
Chebyshev polynomials T_n: orthogonal basis + minimax optimality
Related concepts
- Polynomial ring k[x]
- Legendre polynomials P_n
- Taylor series
- T_2(x) = 2x² − 1: alternation (−1,0,1)→(1,−1,1); roots at ±√2/2
- Chebyshev equioscillation
- Cycle-graph Laplacian spectrum: eigenvalues 2 - 2 cos(2 pi k/N); trace equals 2N (Chebyshev sum identity)
- Spectral methods
- Mass-dependent fractionation line δ¹⁷O = 0.52·δ¹⁸O (TFL anchor)