Chebyshev polynomials

The Chebyshev polynomials Tn(x) of degree n are special orthogonal polynomial functions defined on the domain [-1, 1].

Orthogonality:

-11 W(x) Ti(x) Tj(x) dx = δij
W(x) = (1 – x2)–1/2 (-1 < x < 1)

They obey certain recurrence relations:

Tn(x) = 2 x Tn-1(x) – Tn-2(x)
T0(x) = 1
T1(x) = x

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© djmw, June 20, 1999