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Math Help - Trigonometry simplification

  1. #1
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    Trigonometry simplification

    Can anybody help in simplifying the trigonometric equation under Question 2 in the attached document?

    Thanks
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  2. #2
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    Quote Originally Posted by a_shyam41 View Post
    Can anybody help in simplifying the trigonometric equation under Question 2 in the attached document?

    Thanks
    Your expression is:

    S(x)=\sum_{n=1}^{\infty}a_n \sin \left(\frac{(n+1/2)x}{h}\right)

    where:

     <br />
a_n=\frac{\cos(n\pi)\sqrt{\beta}}{\sqrt{3+\frac{n^  4}{a^4}}}<br />

    First of all observe that \cos(n\pi)=(-1)^n and that \sqrt{\beta} is a constant and so can be taken outside the summation.

     <br />
a_n=a^4 \sqrt{\beta}\frac{(-1)^n}{\sqrt{3a^4+n^4}}<br />

    <br />
S(x)=a^4 \sqrt{\beta}\ \sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{3a^4+n^4}} \sin \left(\frac{(n+1/2)x}{h}\right)<br />

    Next thought is: can we turn this into a Fourier series (that we recognise)? I don't have the time right now but may return to this.

    CB
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