Question

which of the following is not a dirichlet condition for the Fourier series expansion​

Answer 1

Answer:

Dirichlet’s condition for Fourier series expansion is f(x) should be periodic, single valued and finite; f(x) should have finite number of discontinuities in one period and f(x) should have finite number of maxima and minima in a period.

Answer 2

f(x) has a finite number of discontinuities in only one period is not a Dirichlet's condition for the Fourier series expansion​. (Option B)

• The Dirichlet's requirements for the Fourier series expansion are as follows:

1. Over a period, f(x) must be integrable.
2. In every given bounded interval, f(x) must have bounded variation.
3. In every given limited interval, f(x) must have a finite number of discontinuities, and the discontinuities cannot be infinite.

• As a result, the right answer is (b), indicating that f(x) has a finite number of discontinuities in just one period.

It should be noted that the question's alternatives are missing. As a result, the whole question is as follows.

Which of the following is not Dirichlet's condition for the Fourier series expansion?  

(a) f(x) is periodic, single-valued, finite

(b) f(x) has a finite number of discontinuities in only  one period

(c) f(x) has a finite number of maxima and minima