Difference between revisions of "User:Tohline/Math/EQ PminusHalf01"
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[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. | [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. 337, eq. (8.13.1) | ||
</td> | </td> | ||
<td align="center" colspan="3"> | <td align="center" colspan="3"> | ||
[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. | [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. 337, eq. (8.13.2) | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
Revision as of 23:55, 13 June 2018
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<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> |
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Abramowitz & Stegun (1995), p. 337, eq. (8.13.1) |
Abramowitz & Stegun (1995), p. 337, eq. (8.13.2) |
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