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Dear all,

i dont know how to simplify a COMPLEX NUMBER fourier series with LIMITS OF INTEGRATION that are not complementary. I MEAN limits LIKE this X to -X being easy to solve and SIMPLIFY but Not X to -Y or anything different. When i say simplify i mean writing the exponents in the form of cos ωt or sin ωt following the euler's identity.

As an example i will FIND the complex fourier series of the following function and find it unable to simplify.

f(t) = 1, 0 < t < 2

0, 2 < t < 4

MY ATTEMPT at the question.

cn = (1/T) * T/2 - (-T/2) ∫ f(t) * e^-(j2npit/T) dt

= (1/4) * 2 - 0∫e^-(j2npit/T) dt

= (1/4) * [ (-2/jnpi)*e^(-jnpit/2) ] 2 - 0

= (-1/2jnpi)*e^(-jnpi) + (1/j2npi)

=here is my problem!. how do i now write this like in the answer

= answer : -∞ to ∞Ʃ (j/2npi)*(cos npi - 1)e^(jnpit/2)

please tell me a trick for any general question when the limits are NON-COMPLEMENTARY to eacb other when using COMPLEX FOURIER SERIES.

thanks,

do you know a way where i can write my handwitten math work and then post.

this is really tedious.

thanks.

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# Fourier series of complex numbers with diffrent limits of integration?

**Physics Forums | Science Articles, Homework Help, Discussion**