- #1
Morberticus
- 85
- 0
I have a nifty expression
[tex]\frac{1}{r} = \frac{\rm{erf}(r/\alpha)}{r} + \frac{\rm{erfc}(r/\alpha)}{r}[/tex]
I can manipulate it easily enough in one dimension to get a similar expression for [tex]\frac{1}{|r|}[/tex].
Having a little trouble with the expression in three dimensions though[tex]\frac{1}{|\textbf{r}|}[/tex]
Instinctively I want to write
[tex]\frac{1}{|\textbf{r}|} = \frac{\rm{erf}(|\textbf{r}|/\alpha)}{|\textbf{r}|} + \frac{\rm{erfc}(| \textbf{r} |/\alpha)}{|\textbf{r}|}[/tex]
Can I do this? I think I can, as |r| is just a scalar, right?
Thanks
[tex]\frac{1}{r} = \frac{\rm{erf}(r/\alpha)}{r} + \frac{\rm{erfc}(r/\alpha)}{r}[/tex]
I can manipulate it easily enough in one dimension to get a similar expression for [tex]\frac{1}{|r|}[/tex].
Having a little trouble with the expression in three dimensions though[tex]\frac{1}{|\textbf{r}|}[/tex]
Instinctively I want to write
[tex]\frac{1}{|\textbf{r}|} = \frac{\rm{erf}(|\textbf{r}|/\alpha)}{|\textbf{r}|} + \frac{\rm{erfc}(| \textbf{r} |/\alpha)}{|\textbf{r}|}[/tex]
Can I do this? I think I can, as |r| is just a scalar, right?
Thanks