I have some rather technical questions about the complex exponential form of the Fourier series:(adsbygoogle = window.adsbygoogle || []).push({});

1) What is the motivation behind the complex exponential form? Why not just use the real form (i.e. with sine and cosines)?

2) Surely the complex exponential form is an orthogonal set, i.e. [itex] <e^{iπmx/p},e^{iπnx/p}>=0 [/itex] for all integers m,n not equal to one another.

3) Are the two forms equivalent, i.e. if you can express a function with the Fourier sine/cosine series such that the function converges to the Fourier sine/cosine series, then can you also express the same function with its complex exponential Fourier series such that the function converges to its complex exponential Fourier series? And what about the converse?

BiP

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# Complex exponetial form of Fourier series

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