Commit 5b055e8a authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Improvements to the gravity derivative descriptions in the TeX document.

parent c07c0c94
......@@ -18,8 +18,10 @@ by constructing derivatives of the truncated potentials:
\chi^{(4)}(r, r_s) &= \frac{16}{r_s^4} \left(48\alpha(x)^5 - 120\alpha(x)^4 + 100\alpha(x)^3 -30 \alpha(x)^2 + 2\alpha(x)\right) \nonumber \\
\chi^{(5)}(r, r_s) &= \frac{32}{r_s^5} \left(240\alpha(x)^6 - 720\alpha(x)^5 + 780\alpha(x)^4 - 360\alpha(x)^3 + 62\alpha(x)^2 - 2\alpha(x) \right) \nonumber
\end{align}
We can now construct common quantities that appear in derivatives of
multiple orders:
In the Newtonian limit ($r_s\rightarrow\infty$) the first expression
reduces to $\chi(r,r_s) = 1$ whilst all higher-order derivatives
vanish. We can now construct common quantities that appear in
derivatives of multiple orders:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{align}
......
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