Fourier series: complex vs ordinary method

[Nikitin]

Hi! Which is the better method for finding Fourier expansions of a function? The ordinary one (find a_0, b_n and a_n with separate integrals), or the one which uses complex numbers (just find c_n)?

 

[jbunniii]

I generally prefer the method using complex numbers ($c_n$), because the formula is easier to remember. But neither is "better" than the other. Use whichever is easier to evaluate for the specific problem you're working on. For an even or odd function, the real formula may be easier because either the $a_n$'s or the $b_n$'s will all be zero.