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.
2
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real-analysis
fourier-series
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0It's a Fourier Series by definition, since $\log(n)$ is not a function $x$. What's your question? – 2012-04-21
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0See Theorem 4.1 [here](http://books.google.com.au/books?id=gkpUE_m5vvsC&pg=PA24&redir_esc=y#v=onepage&q&f=false). – 2012-04-21
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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