(adsbygoogle = window.adsbygoogle || []).push({}); 1. Find the Fourier sine expansion of [itex]\phi(x)=1[/itex].This was posted in Calculus and Beyond thread, but I realized that this thread may be more appropriate.

2. The attempt at a solution.

I start with [itex]\phi(x)=A_1sin(\pi x)+A_2sin(2\pi x)+\cdots+A_nsin(n\pi x),[/itex] and then add multiply by [itex]A_msin(m\pi x)[/itex] term on each side and integrate from 0 to 1.

So I have [itex]\int\phi(x)A_msin(m\pi x)=\int\left(A_1sin(\pi x)A_msin(m\pi x)+A_2sin(2\pi x)A_msin(m\pi x)+\cdots+A_nsin(n\pi x)A_msin(m\pi x)\right).[/itex]

I know that due to orthogonality you can discard the terms where m is not equal to n (but I don't really understand why so if you can explain this I would appreciate it).

Discarding those terms and using a trig relation I get, [itex]\int\phi(x)A_msin(m\pi x)=1/2\int\left(cos((m-n)\pi x)-cos((m+n)\pi x)\right).[/itex]

I then solve the integral and try to get ##A_m=\frac{4}{\pi}\left(\frac{1}{m}\right),## but I don't know why the answer has only the odd terms.

The book answer is [itex]1=\frac{4}{\pi}\left(sin(\pi x)+\frac{1}{3}sin(3\pi x)+\frac{1}{5}sin(5\pi x) +\cdots\right).[/itex]

Any and all help is greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help with computing/understanding Fourier Sine Expansion.

Loading...

Similar Threads for Help computing understanding |
---|

I Need a help in solving an equation (probably differentiation |

A Understanding dummy variable in solution of 1D heat equation |

**Physics Forums | Science Articles, Homework Help, Discussion**