I need to convert a Fourier cosine series to Chebyshev. I guess the starting point is to Chebyshev expand $\cos(\pi x)$. Is there a closed-form for the Chebyshev coefficients? I expect the answer is yes because the Chebyshev polynomials are like first cousins of the cosines. It's the Chebyshev T polynomials I am referring to.
Any thoughts/ideas anything really welcome. Thanks in advance