Series coefficient for a function can be obtained via Fourier transform:
$$f^{(s)}(0)=\frac{1}{2\pi}\int_{-\infty}^{+\infty} (- i \omega)^s \int_{-\infty}^{+\infty}f(t)e^{i\omega t}dt \, d\omega$$
What is the inverse operator, how to get the original function $f(x)$ if series coefficient $f^{(s)}(0)$ is known, via Fourier transform?