Complex analysis fourier series

In summary, the conversation discusses the task of developing Fourier series for 1/cos(z) and cotan(z) for Im(z)>0, with the speaker expressing uncertainty about how to approach the problem due to the use of complex variables. They refer to previous experience with calculating Fourier series for real functions and mention the possibility of using the Wikipedia page on Fourier series as a starting point.
  • #1
Dassinia
144
0
Hello,

Homework Statement



Develop in Fourier series 1/cos(z) and cotan(z) for Im(z)>0


Homework Equations





The Attempt at a Solution


I really don't know how to do this, i was looking at my notes and we just saw Fourier transform and there is no example for complex functions.
I was thinking to develop cos(z) in exponential form and simplify and then i don't know what to do if someone can "guide" me it'd be great !
Thanks
 
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  • #2
Is that the entire problem statement word for word? It doesn't make sense to me as written.
 
  • #3
Find the Fourier series of the functions 1/cos(z) and cotan(z) for Im(z)>0
this is it.

Thanks
 
  • #4
Do you know what a Fourier series is? If not, that would be the place to start.
 
  • #5
Yes I know and I used to calculate Fourier series for real functions in a previous course.
But for this one z=x+iy so we have two variables so I don't know if I have to calculate the Fourier series according to one of them or both ?
 
  • #6

Related to Complex analysis fourier series

1. What is complex analysis fourier series?

Complex analysis fourier series is a mathematical technique used to represent a periodic function as a sum of sine and cosine functions with complex coefficients. It is an extension of the traditional Fourier series, which only deals with real-valued functions.

2. What is the importance of complex analysis fourier series?

Complex analysis fourier series is important in many areas of mathematics, physics, and engineering. It allows for the representation and analysis of periodic functions that cannot be easily represented by traditional Fourier series. It also has applications in solving differential equations and signal processing.

3. How is complex analysis fourier series different from traditional Fourier series?

Complex analysis fourier series uses complex numbers and complex coefficients to represent periodic functions, while traditional Fourier series only uses real numbers. This allows for a more general representation of periodic functions, including those with complex-valued inputs or outputs.

4. What is the relationship between complex analysis fourier series and complex analysis?

Complex analysis fourier series is a specific application of complex analysis, which is a branch of mathematics that deals with functions on the complex plane. Complex analysis fourier series uses complex analysis techniques to analyze and represent periodic functions.

5. Are there any limitations to using complex analysis fourier series?

Complex analysis fourier series may not be applicable for all types of periodic functions. It is most commonly used for functions that are smooth and well-behaved. Additionally, the convergence of the series may not be guaranteed for all functions, and some modifications may need to be made for certain types of functions.

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