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User:Tohline/Math/EllipticIntegral01 - Revision history
2026-04-27T20:09:14Z
Revision history for this page on the wiki
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Tohline: Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="center" colspan="3"> … of the First Kind </td> </tr> <tr> <td align="right"> <math>~\frac{2K(k)}{\…'
2020-07-15T21:57:55Z
<p>Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="center" colspan="3"> … of the First Kind </td> </tr> <tr> <td align="right"> <math>~\frac{2K(k)}{\…'</p>
<p><b>New page</b></p><div><table border="0" cellpadding="5" align="center"><br />
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&hellip; of the First Kind<br />
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<math>~\frac{2K(k)}{\pi}</math><br />
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<math>~=</math><br />
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<math>~<br />
1 + \biggl( \frac{1}{2} \biggr)^2k^2 <br />
+ \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 k^4 <br />
+ \biggl( \frac{1\cdot 3\cdot 5}{2^4\cdot 3}\biggr)^2 k^6 <br />
+ \biggl( \frac{1\cdot 3\cdot 5 \cdot 7}{2^7 \cdot 3}\biggr)^2 k^8 <br />
+ \cdots<br />
+ \biggl[ \frac{(2n-1)!!}{2^n n!} \biggr]^2 k^{2n}<br />
+ \cdots<br />
</math><br />
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&sect;8.113 and &sect;8.114 of [http://www.mathtable.com/gr/ Gradshteyn &amp; Ryzhik (1965)], &sect;8.113<br />
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</table></div>
Tohline