PG entrance exam IIT JAM 2025 Mock Test Physical Sciences Mathematical Methods of Physics Fourier Transforms and Laplace Transforms
The coefficient bn of f(x) = x at x=L in the Fourier series expansion in the interval (0, 2L) is
1
0
2
\(\frac{2L}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \left( \frac{n \pi x}{L} \right) \)
3
\(\frac{L}{2\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \left( \frac{n \pi x}{L} \right) \)
4
\(\frac{4L}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \left( \frac{n \pi x}{L} \right) \)