Fourier coefficients of sum of two functions with different fundamental periods?

1. How do you find the sum of the Fourier coefficients?
2. What is fundamental period in Fourier series?
3. Can Fourier series coefficients be complex?

How do you find the sum of the Fourier coefficients?

σn(x)=n∑k=0(1−kn+1)Ak(x).

What is fundamental period in Fourier series?

The smallest positive value of T is called the fundamental period. For example, both sin x and cos x have fundamental period 2π, whereas tan x has fundamental period π. A constant function is periodic with arbitrary period T. A function f is even when f(−x) = f(x).

Can Fourier series coefficients be complex?

By contrast, a complex Fourier series aims instead to write f(x) in a series of the following form. starts at −∞), but I am going to gloss over them since we will focus on the case of finite series anyway. Here the numbers cn are complex constants. They are called the complex Fourier coefficients of f(x).