--\left(l+\frac{3}{2}\right) & \text{ for } j=l+\frac{1}{2}\\
-\left(l-\frac{1}{2}\right) & \text{ for } j=l-\frac{1}{2}
+l & \text{for } j=l+\frac{1}{2}\\
+-(l+1) & \text{for } j=l-\frac{1}{2}
+\end{array}\right. \nonumber\\
+&=&\frac{1}{2l+1}\left(lV_{l,l-\frac{1}{2}}(\vec{r})+
+ (l+1)V_{l,l+\frac{1}{2}}(\vec{r})\right)+\nonumber\\
+&&+\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}