diff --git a/examples/theory/multipoles.tex b/examples/theory/multipoles.tex
index e89f4eae802287ba2e51c7d788945b5e47100eab..54665368221e9978fd7605b6c8def1cfc92fa379 100644
--- a/examples/theory/multipoles.tex
+++ b/examples/theory/multipoles.tex
@@ -106,9 +106,9 @@ notation.\\
 
 1-st order:
 \begin{eqnarray}
-D_{(1,0,0)}(\rr) &=& \partial_x \phi(\rr)~=\frac{G}{|\rr|^3}r_x\\
-D_{(0,1,0)}(\rr) &=& \partial_y \phi(\rr)~=\frac{G}{|\rr|^3}r_y\\
-D_{(0,0,1)}(\rr) &=& \partial_z \phi(\rr)~=\frac{G}{|\rr|^3}r_z
+D_{(1,0,0)}(\rr) &=& \partial_x \phi(\rr)~=-\frac{G}{|\rr|^3}r_x\\
+D_{(0,1,0)}(\rr) &=& \partial_y \phi(\rr)~=-\frac{G}{|\rr|^3}r_y\\
+D_{(0,0,1)}(\rr) &=& \partial_z \phi(\rr)~=-\frac{G}{|\rr|^3}r_z
 \end{eqnarray}
 
 2-nd order:
@@ -124,6 +124,23 @@ D_{(0,1,1)} &=& \partial_{yz} \phi(\rr)~= \frac{3Gr_yr_z}{|\rr|^5}\\
 D_{(1,0,1)} &=& \partial_{xz} \phi(\rr)~= \frac{3Gr_xr_z}{|\rr|^5}
 \end{eqnarray}
 
+3-rd order:
+\begin{eqnarray}
+ D_{(3,0,0)} &=& \partial_{xxx} \phi(\rr)~= -\frac{15Gr_x^3}{|\rr|^7} +
+\frac{9Gr_x}{|\rr|^5}\\
+D_{(1,2,0)} &=& \partial_{xyy} \phi(\rr)~= -\frac{15Gr_xr_y^2}{|\rr|^7} +
+\frac{3Gr_x}{|\rr|^5}\\
+D_{(1,0,2)} &=& \partial_{xzz} \phi(\rr)~= -\frac{15Gr_xr_z^2}{|\rr|^7} +
+\frac{3Gr_x}{|\rr|^5}\\
+D_{(2,1,0)} &=& \partial_{xxy} \phi(\rr)~= -\frac{15Gr_x^2r_y}{|\rr|^7} +
+\frac{3Gr_y}{|\rr|^5}\\
+D_{(2,0,1)} &=& \partial_{xxz} \phi(\rr)~= -\frac{15Gr_x^2r_z}{|\rr|^7} +
+\frac{3Gr_z}{|\rr|^5}\\
+D_{(1,1,1)} &=& \partial_{xyz} \phi(\rr)~= -\frac{15Gr_xr_yr_z}{|\rr|^7}
+\end{eqnarray}
+
+
+
 
 \section{B-H potential and accelerations}
 
@@ -168,9 +185,21 @@ The last two expressions are used in the Quickshed example code as well as in
 Bonsai. Gadget only uses the first term in each expression, avoiding the 
 construction of the matrices $\ii{A}$. In practice, the 2-nd order 
 accurate B-H method requires the storage of 10 variables per cell ($M_{{\rm 
-tot},A}, \muu_A, \ii{A}$).
+tot},A}, \muu_A, \ii{A}$).\\
 
-\section{FMM Field tensors}
+The accelerations can also written using Dehnen's short notation:
+
+\begin{eqnarray}
+ a_{i,x} &=& \sum_{\bf n} M_{\bf n}(\muu_A) D_{{\bf n}+(1,0,0)}(\muu_A - 
+\p{i}) \\
+ a_{i,y} &=& \sum_{\bf n} M_{\bf n}(\muu_A) D_{{\bf n}+(0,1,0)}(\muu_A - 
+\p{i}) \\
+ a_{i,z} &=& \sum_{\bf n} M_{\bf n}(\muu_A) D_{{\bf n}+(0,0,1)}(\muu_A - 
+\p{i})
+\end{eqnarray}
+
+
+\section{FMM Field tensors for potential}
 
 Instead of computing the potential and accelerations of each particle, field 
 tensors (generated by the set of particles A) at position $\muu_B$ can 
@@ -187,7 +216,7 @@ following set of expressions.\\
 
 Monopole:
 \begin{eqnarray}
- F_{(0,0,0)}(\muu_B) ~=~ N_B &=& \sum_{|{\bf m}| \leq 2} M_{\bf 
+ F_{(0,0,0)}(\muu_B) ~=~ N_{BA} &=& \sum_{|{\bf m}| \leq 2} M_{\bf 
 m}(\muu_A)D_{{\bf m}}(\rr_{BA}) \\
 &=&  M_{(0,0,0)}(\muu_A)D_{(0,0,0)}(\rr_{BA})\\ 
 & & +M_{(2,0,0)}(\muu_A)D_{(2,0,0)}(\rr_{BA}) \\
@@ -196,15 +225,15 @@ m}(\muu_A)D_{{\bf m}}(\rr_{BA}) \\
 &=&M_{{\rm tot}, A}\phi(\rr_{BA}) + 
 \frac{1}{2}\sum_{\alpha,\beta}I_{A,\alpha\beta}\partial_{\alpha\beta}\phi(\rr_{
 BA }) \\
-&=& \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|} -\frac{1}{2}\frac{{\rm 
+&=& \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|} -\frac{G}{2}\frac{{\rm 
 tr}(\ii{A})}{|\rr_{BA}|^3} + 
-\frac{3}{2}\frac{\rr_{BA}^T \cdot 
+\frac{3G}{2}\frac{\rr_{BA}^T \cdot 
 \ii{A} \cdot \rr_{BA}}{|\rr_{BA}|^5}
 \end{eqnarray}
 
 Dipole:
 \begin{eqnarray}
-  F_{(1,0,0)}(\muu_B) ~=~ Q_{B,x} &=& \sum_{|{\bf m}| \leq 1} M_{\bf 
+  F_{(1,0,0)}(\muu_B) ~=~ Q_{BA,x} &=& \sum_{|{\bf m}| \leq 1} M_{\bf 
 m}(\muu_A)D_{{\bf 
 m}+(1,0,0)}(\rr_{BA}) \\
 &=&  M_{(0,0,0)}(\muu_A)D_{(1,0,0)}(\rr_{BA})\\ 
@@ -214,7 +243,7 @@ m}+(1,0,0)}(\rr_{BA}) \\
 
 Quadrupole (diagonal term):
 \begin{eqnarray}
- F_{(2,0,0)}(\muu_B)~=~ J_{B,xx} &=& \sum_{|{\bf m}| \leq 0} M_{\bf 
+ F_{(2,0,0)}(\muu_B)~=~ J_{BA,xx} &=& \sum_{|{\bf m}| \leq 0} M_{\bf 
 m}(\muu_A)D_{{\bf 
 m}+(2,0,0)}(\rr_{BA}) \\
 &=& M_{(0,0,0)}(\muu_A)D_{(2,0,0)}(\rr_{BA}) \\
@@ -226,7 +255,7 @@ m}+(2,0,0)}(\rr_{BA}) \\
 
 Quadrupole (off-diagonal term):
 \begin{eqnarray}
- F_{(1,1,0)}(\muu_B)~=~J_{B,xy} &=& \sum_{|{\bf m}| \leq 0} M_{\bf 
+ F_{(1,1,0)}(\muu_B)~=~J_{BA,xy} &=& \sum_{|{\bf m}| \leq 0} M_{\bf 
 m}(\muu_A)D_{{\bf 
 m}+(1,1,0)}(\rr_{BA}) \\
 &=& M_{(0,0,0)}(\muu_A)D_{(1,1,0)}(\rr_{BA}) \\
@@ -236,16 +265,48 @@ m}+(1,1,0)}(\rr_{BA}) \\
 
 All these terms can be written using a more compact notation.
 \begin{eqnarray}
-N_B &=&  \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|} -\frac{1}{2}\frac{{\rm 
+N_{BA} &=&  \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|} -\frac{G}{2}\frac{{\rm 
 tr}(\ii{A})}{|\rr_{BA}|^3} + 
-\frac{3}{2}\frac{\rr_{BA}^T \cdot 
+\frac{3G}{2}\frac{\rr_{BA}^T \cdot 
 \ii{A} \cdot \rr_{BA}}{|\rr_{BA}|^5} \\
-\qq{B} &=&  \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^3} \rr_{BA}\\
-\jj{B} &=& \frac{3GM_{{\rm tot}, A}}{|\rr_{BA}|^5} \rr_{BA} 
+\qq{BA} &=&  \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^3} \rr_{BA}\\
+\jj{BA} &=& \frac{3GM_{{\rm tot}, A}}{|\rr_{BA}|^5} \rr_{BA} 
 \otimes\rr_{BA} - \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^3} \identity
 \end{eqnarray}
 
+Note that $\jj{B}$ is symmetric, meaning that $10$ additional numbers per cell 
+only have to be stored. That is a total of $10$ for the multipoles and $10$ for 
+the field tensors.
 
+\section{Gravitational potential in FMM}
+
+The potential at the position $\p{i}$ in the vicinity of $\muu_B$ due to the 
+mass clustered around $\muu_A$ can be computed using the field tensors created 
+by the mutipoles at position $\muu_A$ on the position $\muu_B$.
+
+\begin{equation}
+ \phi_A(\p{i}) = \sum_{|{\bf n}| \leq2} \frac{1}{ {\bf n}!} (\p{i} - 
+\muu_B)^{\bf n} F_{\bf n}(\muu_B)
+\end{equation}
+
+Setting $\dd_{i,B}= \p{i} - \muu_B$ and $\rr_{BA} = \muu_B - \muu_A$, this sum 
+expands into
+
+\begin{eqnarray}
+ \phi_A(\p{i}) &=& N_{BA} + \dd_{i,B}\cdot\qq{BA} + \dd_{i,B}^T \cdot \jj{BA} 
+\cdot \dd_{i,B} \\
+&=& \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|} -\frac{1}{2}\frac{{\rm 
+tr}(\ii{A})}{|\rr_{BA}|^3} + 
+\frac{3}{2}\frac{\rr_{BA}^T \cdot 
+\ii{A} \cdot \rr_{BA}}{|\rr_{BA}|^5} \\
+& &+ \frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^3} \rr_{BA}\cdot\dd_{i,B} \\
+& &+\frac{3}{2}\frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^5} \left(\dd_{i,B}^T \cdot 
+\rr_{BA}\otimes\rr_{BA}\cdot \dd_{i,B}\right) \\
+& & - \frac{1}{2}\frac{GM_{{\rm tot}, A}}{|\rr_{BA}|^3} \left(\dd_{i,B}^T 
+\cdot\identity \cdot \dd_{i,B}\right)
+\end{eqnarray}
 
+Note that if $\p{i}=\muu_B$ (i.e. $d_{i,B}={\bf 0}$), the expression for the 
+potential in the B-H formalism is recovered.
 
 \end{document}