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Idea

Chebyshev polynomials are polynomials that are often used in approximations, for example in spectral methods.

An approximation with Chebyshev polynomials is essentially the same as an approximation with a Fourier series after a change of variable.

The mapping is:

When we write the Chebyshev polynomials $T_n$ as functions of $\theta$:

then the following series are equivalent:

and

References

• Chebyshev polynomials, Wikipedia