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Questions on the functionality operating on polynomials

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Fittind data with shifted Chebyshev polynomials

I am trying to fit data from a simulation to a particular class of polynomials, according to least squares approach. data = Import["Mathematica file.txt", "Table"] The polynomials are the shifted Chebyshev … polynomials, that is: $${\displaystyle T_{n}^{*}(x)=T_{n}(2x-1)~.}$$ How could one use Mathematica to find the coefficients $a_0$, $a_1$ and so on in: $$\sum_{n=0}^N a_n T_{n}(2x-1)$$ which fits the imported …
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