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I want to show $\displaystyle \sum_{n=2}^{\infty}\frac{\cos nx}{\log n}$ is a Fourier series but i am stuck how to show the given series is a Fourier series. Can anybody help me?

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It's a Fourier Series by definition, since $\log(n)$ is not a function $x$. What's your question? – nbubis Apr 21 '12 at 12:05
See Theorem 4.1 here. – Ragib Zaman Apr 21 '12 at 12:07
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@nbubis He wants to show there is actually some function with that Fourier series, not just that it is of the form that Fourier series are in. If you replaced $\cos nx$ with $\sin nx$ the theorem I linked to shows there is no function with that Fourier series. – Ragib Zaman Apr 21 '12 at 12:08

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