Question

In Parseval’s formula for half range Fourier series, the formula contains l/2 multiplied with the square of individual coefficients.

(a) True

(b) False

This question was posed to me during an interview for a job.

I need to ask this question from Fourier Half Range Series topic in portion Fourier Series of Engineering Mathematics

Answer 1

The correct option is (a) True

For explanation: The Parseval’s formula for half range Fourier cosine series is \(\int_0^l(f(x))^2 dx=\frac{l}{2} [\frac{a_0^2}{2}+∑_{n=1}^∞(a_n^2)] \)

The Parseval’s formula for half range Fourier sine series is \(\int_0^l(f(x))^2 dx=\frac{l}{2} ∑_{n=1}^∞(b_n^2) .\)