Difference between revisions of "User:Tohline/Math/EQ PminusHalf01"
Jump to navigation
Jump to search
| Line 13: | Line 13: | ||
<td align="left"> | <td align="left"> | ||
<math>~ | <math>~ | ||
\frac{2}{\pi} \biggl[\frac{2}{z+1}\biggr]^{1 / 2} ~K\biggl( \sqrt{ \frac{z-1}{z+1}} \biggr) | \frac{2}{\pi} \biggl[\frac{2}{z+1}\biggr]^{1 / 2} ~K\biggl( \sqrt{ \frac{z-1}{z+1}} \biggr) | ||
</math> | </math> | ||
</td> | </td> | ||
<td align="center" rowspan="2" width="15%">… for example …</td> | |||
<td align="right"> | |||
[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Special_Function_Relationships]] | |||
</td> | |||
<td align="right"> | |||
<math>~P_{-1 / 2}(\cosh\eta)</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~ | |||
\biggl[ \frac{\pi}{2} ~ \cosh \frac{\eta}{2} \biggr]^{-1} K\biggl( \tanh \frac{\eta}{2} \biggr) | |||
</math> | |||
</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td align="center" colspan="4"> | <td align="center" colspan="4"> | ||
[https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. 334, eq. (8.13.1) | [https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. 334, eq. (8.13.1) | ||
</td> | |||
<td align="center" colspan="4"> | |||
[https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. 334, eq. (8.13.2) | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
Revision as of 22:37, 13 June 2018
|
|
<math>~P_{-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_{-1 / 2}(\cosh\eta)</math> |
<math>~=</math> |
<math>~ \biggl[ \frac{\pi}{2} ~ \cosh \frac{\eta}{2} \biggr]^{-1} K\biggl( \tanh \frac{\eta}{2} \biggr) </math> |
|
Abramowitz & Stegun (1995), p. 334, eq. (8.13.1) |
Abramowitz & Stegun (1995), p. 334, eq. (8.13.2) |
|||||||
