Why can we express any function in terms of cosine (Fourier) and polynomial (Taylor)? what is special about cosine and polynomial?
I mean can we write any function in terms of exponential (e^x) instead of cosine and polynomial for example?
2026-05-16 07:33:57.1778916837
What's special about cosine and polynomial?
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The premise of your question is flawed: You can't express ANY function in terms of cosine / polynomials. Not even in terms of converging infinite series of such terms.
I suggest you read the inluminating https://en.wikipedia.org/wiki/Convergence_of_Fourier_series for further details about what is required for such series to converge.