# Thread: ln|2sin(x)|

1. ## ln|2sin(x)|

Hello everybody

Could any one help me to prove the series expansion in the photo below ?

Thanks in Advance and best regards

2. ## Re: ln|2sin(x)|

What methodology are you using for series expansion? I ask because this looks like a Fourier series.

3. ## Re: ln|2sin(x)|

Thanks for replay

I am trying to solve the integration [ int( ln|1-sin(x)|) dx ] , and i have asked one of my friends and he solved this integration as in the photo attached here , he mention in this solving about this series expansion , i have test it numerically , it is true but how we can prove it ?

Thanks in advance

4. ## Re: ln|2sin(x)|

maybe start with

$\sum _{n=1}^{\infty } \frac{e^{i 2n x}}{n}$

5. ## Re: ln|2sin(x)|

Originally Posted by razi1974
Thanks for replay

I am trying to solve the integration [ int( ln|1-sin(x)|) dx ] , and i have asked one of my friends and he solved this integration as in the photo attached here , he mention in this solving about this series expansion , i have test it numerically , it is true but how we can prove it ?

Thanks in advance
It is a Fourier series expansion. Look up Fourier series. If you have not seen that before, it is probably beyond your current course.

6. ## Re: ln|2sin(x)|

Thanks Dear Slip and Idea for replay

Yes , i know about it , but i have to refresh my memory .

Really thank you so much .

Best regards