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Description
This object implements the NcWindow class for a top-hat window function.
This object returns the top hat window function in the real space. \begin{align} W_{TH}(r, R) = \frac{3}{4\pi R^3} \left{ \begin{array} {ll} 1 & \leq R\ 0 & > R. \end{array} \right. \end{align} The mass enclosed within the volume selected by this window function is $M_{TH}(R)= \frac{4\pi}{3}\overline{\rho} R^3$,where $\overline{\rho}(z)$ is the mean density of the universe at redshift $z$.
The top-hat window function in the Fourier space is given by
\begin{align} W_{th}(k, R) &= \frac{3}{(kR)^3}(\sin kR - (kR)\cos kR) \ &= \frac{3}{(kR)} j_1(kR), \end{align} where $j_\nu(kR)$ is the spherical Bessel function.
The first derivative with respect to $R$ \begin{equation} \frac{dW_{TH}(k, R)}{dR} = \frac{-9}{k^3 R^4} (\sin kR - (kR)\cos kR) + \frac{3}{k R^2} \sin kR. \end{equation}
Functions
nc_window_tophat_new ()
NcWindow * nc_window_tophat_new ();
This function returns a NcWindow with a NcWindowTophat implementation.