= Band-limited linear density correlation
{title2=$\xi(r)=\dfrac{A}{2\pi^2r^4}[-K^2\cos K+2K\sin K+2(\cos K-1)]$}
For an isotropic <matter power spectrum> $P(k)=Ak$ on $0\leq k\leq k_{\max}$ and zero elsewhere, put $K=k_{\max}r$. Angular integration of the <Fourier transform> gives $\xi(r)=A(2\pi^2r)^{-1}\int_0^{k_{\max}}k^2\sin(kr)\,dk$, and two integrations by parts yield the displayed answer. Its apparent origin singularity is removable, with $\xi(0)=Ak_{\max}^4/(8\pi^2)$. The sharp cutoff creates oscillatory, including negative, correlations without violating positivity of the spectrum.
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