Question

What is the Fourier series expansion of the function f(x) in the interval (c, c+2π)?

(a) \(\frac{a_0}{2}+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \)

(b) \(a_0+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \)

(c) \(\frac{a_0}{2}+∑_{n=0}^∞ a_n cos(nx) +∑_{n=0}^∞ b_n sin(nx) \)

(d) \(a_0+∑_{n=0}^∞ a_n cos(nx) + ∑_{n=0}^∞ b_n sin(nx) \)

The question was posed to me during a job interview.

My question is from Fourier Series Expansions topic in section Fourier Series of Engineering Mathematics

Answer 1

Right option is (a) \(\frac{a_0}{2}+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \)

For explanation I would say: Fourier series expantion of the function f(x) in the interval (c, c+2π) is given by \(\frac{a_0}{2}+∑_{n=1}^∞ a_n cos(nx) +∑_{n=1}^∞ b_n sin(nx) \) where, a0 is found by using n=0, in the formula for finding an. bn is found by using sin(nx) instead of cos(nx) in the formula to find an.