Tabellenanhang - Familie Alex, Weingarten

O.3. FORMELN IM QUELLTEXT 73
\begin{equation}
\tau_{tur} = \rho l^2 \; | \frac{\partial \bar{v_1}}
{\partial x_2} | \; \frac{\partial \bar{v_1}}{\partial x_2}
\end{equation}
\begin{eqnarray}
\label{formel}
\ddot R & = & \frac{1}{\Psi} ( V_r - \dot R)
+ R {\dot \Phi}^2 \nonumber\\
\ddot \Phi & = & \big\lbrack \frac{1}{\Psi}
(V_\varphi - R \dot \Phi )
- 2 \dot R \dot \Phi \big\rbrack \frac{1}{R} \\
\ddot Z & = & \frac{1}{\Psi}(V_Z-\dot Z) \nonumber\\
\nonumber
\end{eqnarray}
\begin{equation}
{\hat\chi}^2 = \frac{n(n-1)}{B(n-B)} \sum_{i=1}^k
\frac{(B_i - E_i)^2}{n_i} > \chi_{k-1;\alpha}^2
\end{equation}
\begin{equation}
V(r,\vartheta,\varphi)=\sum\limits_{l=0}^\infty
\frac{4\pi}{2l+1}
\sum\limits_{m=-l}^l \, q_{l,m} \frac{Y_{l,m}
\vartheta,\varphi)}{r^{l+1}}
\end{equation}
\begin{eqnarray}
\vec{q}= \left(\begin{array}{c}
q_{0,0}\\
q_{1,1}\\q_{1,0}\\q_{1,-1}\\
q_{2,2}\\q_{2,1}\\q_{2,0}\\q_{2,-1}\\q_{2,-2}\\
\end{array} \right)
\end{eqnarray}
\begin{equation}
q’_{l’,m’}=\sum\limits_{o=0}^\infty\sum\limits_{p=-o}^o
n_{o,p} \; q_{o,p} \; (\nabla)_{l’+o,m’-p;o,p} \,
\frac{Y_{l’+o,m’-p}(\vartheta_a,\varphi_a)}{a^{l’+o+1}}
\end{equation}
\begin{equation}
q_{l,m}= -q’_{l,m} R^{2l+1} \,
\frac{l(\epsilon_i-\epsilon_a)}
{l(\epsilon_a+\epsilon_i)+\epsilon_a}
\end{equation}
\begin{eqnarray}
\vec{q’}_{1,1}=\vec{q’}_{1,0}+I_{2,1} \; \vec{q’}_{2,0}\\[0.3cm]
\vec{q’}_{2,1}=\vec{q’}_{2,0}+I_{1,2} \; \vec{q’}_{1,0}
\end{eqnarray}
\begin{eqnarray}
\lefteqn{\nabla_{\pm 1} \sum\limits_{l=0}^{\infty}
\frac{4\pi}{2l+1} \,