Complex Fourier series of sin (t)

[unscientific]

In finding C_n, I arrived at a different answer. I got an extra factor of (1/i) instead, which came when you do the integral of each exponential with respect to t; so you get a factor of 1/i(1-n) and 1/i(1+n) respectively..

Did they intentionally leave that out?

 

[mathman]

http://www.math24.net/complex-form-of-fourier-series.html

The above may help.

This should be in one of the math forums.

 

[mathman]

Addition thought. f(t) = sint is its own Fourier series. exp(it) = cost + isint. Therefore c₁ needs a coefficient 1/i. I can't see what your disagreement is about. Perhaps you can give the details of your derivation.

 

[unscientific]

Addition thought. f(t) = sint is its own Fourier series. exp(it) = cost + isint. Therefore c₁ needs a coefficient 1/i. I can't see what your disagreement is about. Perhaps you can give the details of your derivation.

Sorry, I spotted my mistake!

 

[PJC01]

It is possible that the extra factor of (1/i) was intentionally left out in order to simplify the expression or to make it easier to work with. However, it could also be a mistake or oversight. In any case, it is important to carefully check all steps and factors when solving complex Fourier series to ensure accuracy. It is also important to consider the overall context of the problem and whether the extra factor makes sense in that context. If you are unsure, it may be helpful to consult with a colleague or reference material to confirm your solution.