Chebyshev polynomials of the first kind

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Chebyshev polynomials, which are often written Tn(x), are a set orthogonal polynomials defined as the solutions to Chebyshev's differential equation

Chebyshev's differential equation

(1-x2)y''-xy'+n2y = 0

n = 0, 1, 2, ...

The first five Chebyshev polynomials are:

T0(x) = 1

T1(x) = x

T2(x) = 2x2 - 1

T3(x) = 4x3 - 3x

T4(x) = 8x4 - 8x2 + 1

These are plotted from -1 to +1 above.

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This page was last changed on: 04 December 2017.

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