We present an approximation for efficient calculation of the Lindhard susceptibility $chi^{L}(q,omega)$ in a periodic system through the use of simple products of real space functions and the fast Fourier transform (FFT). The method is illustrated by providing $chi^{L}(q,omega)$ results for the electron doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ extended over several Brillouin zones. These results are relevant for interpreting inelastic X-ray scattering spectra from cuprates.
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