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Thread: ln|2sin(x)|

  1. #1
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    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
    Attached Thumbnails Attached Thumbnails ln|2sin(x)|-lnsin-x-.jpg  
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  2. #2
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    Re: ln|2sin(x)|

    What methodology are you using for series expansion? I ask because this looks like a Fourier series.
    Last edited by SlipEternal; Nov 3rd 2017 at 07:46 AM.
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  3. #3
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    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
    Attached Thumbnails Attached Thumbnails ln|2sin(x)|-series.jpg  
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  4. #4
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    Re: ln|2sin(x)|

    maybe start with

    \sum _{n=1}^{\infty } \frac{e^{i 2n x}}{n}
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  5. #5
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    Re: ln|2sin(x)|

    Quote Originally Posted by razi1974 View Post
    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.
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  6. #6
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    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
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