For a function $f$ with period $P$ the Fourier series is $$f(x)=\sum_{n=1}^\infty{a_n\cos\left(\frac{2\pi n x}{P}\right)+b_n\sin\left(\frac{2\pi n x}{P}\right)}$$
I want to modify the function to be
$$g(x)=\sum_{n=1}^\infty{a_n\cos\left(\frac{2\pi(\ln{n})x}{P}\right)+b_n\sin\left(\frac{2\pi(\ln{n})x}{P}\right)}$$
Is there a modified application of the properties of Fourier series and/or transform that can be formed for this type of function?
Edit I made some edits but my question is still the same.