NumCosmoMathPowspecvar_tophat_R

This function computes the value of the linearly extrapolated rms fluctuations of mass in a sphere of radius $R$ applying a top-hat filter at redshift $z$, $$\sigma_{R}^{2}(z) = \frac{1}{2\pi^2} \int_{k_{\mathrm{min}}}^{k_\mathrm{max}} W^{2}{TH}(kR) \, P(k,z) \, k^2 \, \mathrm{d}k \, .$$ Where, $W{TH}(t)$ is the top-hat filter in Fourier space, $$W_{TH}(t) = \frac{3}{t^3} \left( \sin t - t \cos t \right) = \frac{3}{t} j_{1}(t),$$ and $j_1(t)$ is the first order spherical Bessel function of the first kind. This function is recommended for a small set of $z$ and $R$ values. For a wide range of values it is best to apply NcmPowspecFilter, instead.