Chebyshev polynomials

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The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, denoted as T n ( x ) {\displaystyle T_{n}(x)} and U n ( x ) {\displaystyle U_{n}(x)} . They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T n {\displaystyle T_{n}} are defined by T n ( cos ⁡ θ ) = cos ⁡ ( n θ ) . {\displaystyle T_{n}(\cos \theta )=\cos(n\theta...

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