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Thread: Summing a Trig function

  1. #1 Summing a Trig function 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    can anyone help me sum this summation?



    thanks


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  3. #2  
    Forum Ph.D. william's Avatar
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    I'm too lazy to try to work it out, but my first thought is to use Euler's formula and keep the imaginary components and see if it works into a sum with a ready answer. As my initial guesses usually go though... I'm probably wrong.


    "... the polhode rolls without slipping on the herpolhode lying in the invariable plane."
    ~Footnote in Goldstein's Mechanics, 3rd ed. p. 202
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  4. #3  
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    Quote Originally Posted by william
    I'm too lazy to try to work it out, but my first thought is to use Euler's formula and keep the imaginary components and see if it works into a sum with a ready answer. As my initial guesses usually go though... I'm probably wrong.
    It will work. The exponentials form a finite geometric sum. It is slightly tedious to then separate the real and imaginary parts.
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