Difference between revisions of "User:Tohline/Math/EQ EllipticIntegral02"
Jump to navigation
Jump to search
| Line 25: | Line 25: | ||
<tr> | <tr> | ||
<td align="center" colspan="4"> | <td align="center" colspan="4"> | ||
[http://www.mathtable.com/gr/ Gradshteyn & Ryzhik (1965)], §8.114 | [http://www.mathtable.com/gr/ Gradshteyn & Ryzhik (1965)], §8.114.1 | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
Latest revision as of 20:44, 16 July 2020
|
|
<math>~\frac{2E(k)}{\pi}</math> |
<math>~=</math> |
<math>~ 1 - \frac{1}{2^2} ~k^2 - \frac{1^2\cdot 3}{2^2\cdot 4^2}~ k^4 - \biggl(\frac{1\cdot 3\cdot 5}{2^4\cdot 3}\biggr)^2~\frac{ k^6 }{5} - \biggl( \frac{1\cdot 3\cdot 5 \cdot 7}{2^7 \cdot 3}\biggr)^2 \frac{k^8}{7} ~-~ \cdots - \biggl[ \frac{(2n-1)!!}{2^n n!} \biggr]^2 \frac{k^{2n}}{2n-1}
~-~ \cdots </math> |
|
Gradshteyn & Ryzhik (1965), §8.114.1 |
|||
