Assume you are provided with the following Fourier Coefficients for a function on the interval of [-πT,π]: A‚ = 5, a₁ = (10/π); a3 = (-10/3 π), a5 = (1957), az, a4, b₁,b2, 63, 64, 65 are all zero. If you know that E is the partial sum of the Fourier series up to the kth and

You want to find the Fourier series for the funtion tan(x) over the interval -2π to 2π. Will the Fourier series converge? Prove your answer quantitatively.

Find the Fourier series of the following functions (on [-π, π]). (1) sin²x. (2) r. Also sketch the curve of the Fourier series (on [-37, 3π]). Repeat the above problem on [-L, L].

Please show a step-by-step solution. Do not skip steps, and explain your steps.