# Answer to Question #38 in MatLAB | Mathematica | MathCAD | Maple for Shaun McKnight

Question #38

The degree-n Chebyshev polynomial is defined by

Tn(x) = cos[ncos-1(x)], -1 <= x <= 1.

These satisfy To(x) = 1, T1(x) = x, and the recursion relation

Tn+1(x) = 2xTn(x) - Tn-1(x), n >= 1.

Write a function Chebeval (x,N) that evaluates all of the Chebyshev polynomials of degree less than or equal to N at all of the points in column vector x. The result should be an array of size length (x) by N+1.

Tn(x) = cos[ncos-1(x)], -1 <= x <= 1.

These satisfy To(x) = 1, T1(x) = x, and the recursion relation

Tn+1(x) = 2xTn(x) - Tn-1(x), n >= 1.

Write a function Chebeval (x,N) that evaluates all of the Chebyshev polynomials of degree less than or equal to N at all of the points in column vector x. The result should be an array of size length (x) by N+1.

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