06/23/2010, 01:20 AM
\( f(e^x) \) can be expressed as a Fourier series, but then how do you express the right hand side? If it's a Taylor series, you can't just equate coefficients, since what they're multiplying is different! E.g. \( 3e^{2x} \ne 3x^2 \). Just because the coefficients are equal doesn't mean the terms are equal. Equating coefficients of the two distinct series types will not produce a solution of the equation. I don't see what you're trying to get at here...