- #1
Nikitin
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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)?
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The complex Fourier series method represents a periodic function as a combination of complex exponential functions, while the ordinary method uses trigonometric functions. This leads to a more compact and elegant representation of the function in the complex method, but both methods ultimately achieve the same result.
The complex Fourier series method is more commonly used in scientific applications due to its compact representation and the ability to easily handle periodic functions with discontinuities.
No, the complex Fourier series method can only be applied to periodic functions. For non-periodic functions, other methods such as the Fourier transform must be used.
The choice between complex and ordinary Fourier series method depends on the nature of the function being represented and the goal of the analysis. For simple periodic functions, the ordinary method may suffice, while for more complex functions, the complex method may be more suitable.
The complex Fourier series method offers a more concise and elegant representation of periodic functions, making it easier to analyze and manipulate them mathematically. It also allows for the handling of functions with discontinuities, which the ordinary method may struggle with.