Fourier series coeffecients

  • Engineering
  • Thread starter lottotlyl
  • Start date
  • #1
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Homework Statement:

how did my prof get the last term after the third equal sign

Relevant Equations:

fourier series coeffecient equation
i tired using complex identity equation for sin(pi*k/3) but it doesn't work out
 

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Answers and Replies

  • #2
359
172
Applying the fundamental theorem of calculus which says that
$$\int_a^b f(t)dt=F(t)\Big|_a^b=F(b)-F(a)$$ where ##F(t)## is a function satisfying $$\frac{dF(t)}{dt}=f(t).$$
Then you also need to use elemental algebra and complex analysis.
 
  • #4
359
172
Well, notice that in the final answer you have the term $$e^{\frac{-j\pi k}{3}}$$ so it would be a good idea to multiply by $$1=e^{\frac{-j\pi k}{3}}e^{\frac{j\pi k}{3}}.$$
 

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