-&&+\frac{1}{2l+1}\left\{\begin{array}{rl}
-l\left(V_{l,l+\frac{1}{2}}(\vec{r})-V_{l,l-\frac{1}{2}}(\vec{r})\right) &
- \text{for } j=l+\frac{1}{2}\\
--(l+1)\left(V_{l,l+\frac{1}{2}}(\vec{r})-V_{l,l-\frac{1}{2}}(\vec{r})\right) &
- \text{for } j=l-\frac{1}{2}
+&&\frac{1}{2l+1}
+\left(V_{l,l+\frac{1}{2}}(\vec{r})-V_{l,l-\frac{1}{2}}(\vec{r})\right)
+\cdot\left\{\begin{array}{c}
+l \\
+-(l+1)
+\end{array}\right. \nonumber\\
+&=&\left\{\begin{array}{cl}
+V_{l,l+\frac{1}{2}}(\vec{r}) & \text{for } j=l+\frac{1}{2}\\
+V_{l,l-\frac{1}{2}}(\vec{r}) & \text{for } j=l-\frac{1}{2}