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?
To show $\displaystyle\sum_{n=2}^{\infty}\frac{\cos nx}{\log n}$ is a Fourier series.
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real-analysis
fourier-series
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2@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. – 2012-04-21