06/23/2010, 10:52 PM
(06/23/2010, 01:20 AM)mike3 Wrote: \( f(e^x) \) 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...
yes , but the thing is this : we compute the fourier coefficients with the taylor expression and the n'th derivate of the four series.
this crossed self-reference might be solvable directly or recursively.
regards
tommy1729