Difference between revisions of "User:Tohline/Math/EQ PminusHalf01"
Jump to navigation
Jump to search
| Line 6: | Line 6: | ||
</td> | </td> | ||
<td align="right"> | <td align="right"> | ||
<math>~P_{-1 | <math>~P_{-\frac{1}{2}}(z)</math> | ||
</td> | </td> | ||
<td align="center"> | <td align="center"> | ||
| Line 20: | Line 20: | ||
<td align="right"> | <td align="right"> | ||
<math>~P_{-1 | <math>~P_{-\frac{1}{2}}(\cosh\eta)</math> | ||
</td> | </td> | ||
<td align="center"> | <td align="center"> | ||
| Line 27: | Line 27: | ||
<td align="left"> | <td align="left"> | ||
<math>~ | <math>~ | ||
\biggl[ \frac{\pi}{2} | \biggl[ \frac{\pi}{2} \cdot \cosh \frac{\eta}{2} \biggr]^{-1} K\biggl( \tanh \frac{\eta}{2} \biggr) | ||
</math> | </math> | ||
</td> | </td> | ||
Revision as of 18:30, 14 June 2018
|
|
<math>~P_{-\frac{1}{2}}(z)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi} \biggl[\frac{2}{z+1}\biggr]^{1 / 2} ~K\biggl( \sqrt{ \frac{z-1}{z+1}} \biggr) </math> |
for example … |
<math>~P_{-\frac{1}{2}}(\cosh\eta)</math> |
<math>~=</math> |
<math>~ \biggl[ \frac{\pi}{2} \cdot \cosh \frac{\eta}{2} \biggr]^{-1} K\biggl( \tanh \frac{\eta}{2} \biggr) </math> |
|
Abramowitz & Stegun (1995), p. 337, eq. (8.13.1) |
Abramowitz & Stegun (1995), p. 337, eq. (8.13.2) |
||||||
