Eli
This is the full window-integrated counts transfer function, which can be used to compute the tomographic angular power spectrum:
\begin{multline}\tag{1}
\Delta^W_{N,l}(k) =
\int_{0}^{\eta_A}\!{\rm d}\eta \biggl[
W(\eta)\left(\delta_N j_l(k\chi) + \frac{k v}{\mathcal{H}} j_l{}''(k\chi)\right)
+ W_{\delta\eta}(\eta)\left[ \psi j_l(k\chi) + v j_l'(k\chi) \right]
+(\dot{\psi} + \dot{\phi})j_l(k\chi)\int_0^\eta W_{\delta\eta}(\eta'){\rm d}\eta' \\
+(\phi+\psi)j_l(k\chi)\left( \int_0^\eta (2-5s) \frac{W(\eta')}{\chi'}{\rm d}\eta'
+\frac{l(l+1)}{2} \int_0^\eta \frac{\chi'-\chi}{\chi\chi'}(2-5s)W(\eta'){\rm d}\eta' \right) \\
+ W(\eta)j_l(k\chi) \left(\frac{1}{\mathcal{H}}\dot{\phi} +\psi + (5s-2)\phi\right)
\biggr],\\
\\
\end{multline}
where
\begin{equation}\tag{2}
W_{\delta\eta}(\eta) \equiv \left[\frac{2-5s}{\mathcal{H}\chi} + 5s- \frac{\partial \ln [a^3 \bar{N}(L>\bar{L}_{s*})]}{\mathcal{H}\partial \eta} + \frac{\dot{\mathcal{H}}}{\mathcal{H}^2}\right]_\eta W(\eta),
\end{equation}
and
\begin{align}\tag{3}
\chi' = \eta_A - \eta', \ \chi = \eta_A - \eta.
\end{align}
Therefore, we can reference the multiline Equation (1), and Equations (2 - 3).
