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2026-05-01T13:44:29Z
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https://www.vistrails.org//index.php?title=User:Tohline/Math/EQ_EllipticIntegral03&diff=20211&oldid=prev
Tohline at 20:47, 16 July 2020
2020-07-16T20:47:16Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:47, 16 July 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\ln \frac{4}{k^'} + \frac{1}{2^2}\biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} \biggr)<del style="font-weight: bold; text-decoration: none;">{</del>k'<del style="font-weight: bold; text-decoration: none;">}</del>^2</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\ln \frac{4}{k^'} + \frac{1}{2^2}\biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} \biggr)<ins style="font-weight: bold; text-decoration: none;">(</ins>k'<ins style="font-weight: bold; text-decoration: none;">)</ins>^2</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} \biggr)<del style="font-weight: bold; text-decoration: none;">{</del>k'<del style="font-weight: bold; text-decoration: none;">}</del>^4</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} \biggr)<ins style="font-weight: bold; text-decoration: none;">(</ins>k'<ins style="font-weight: bold; text-decoration: none;">)</ins>^4</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ \biggl( \frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} - \frac{2}{5\cdot 6} \biggr)<del style="font-weight: bold; text-decoration: none;">{</del>k'<del style="font-weight: bold; text-decoration: none;">}</del>^6 + \cdots</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ \biggl( \frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} - \frac{2}{5\cdot 6} \biggr)<ins style="font-weight: bold; text-decoration: none;">(</ins>k'<ins style="font-weight: bold; text-decoration: none;">)</ins>^6 <ins style="font-weight: bold; text-decoration: none;">~</ins>+<ins style="font-weight: bold; text-decoration: none;">~ </ins>\cdots</div></td></tr>
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Tohline
https://www.vistrails.org//index.php?title=User:Tohline/Math/EQ_EllipticIntegral03&diff=20207&oldid=prev
Tohline: Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templat…'
2020-07-16T20:37:55Z
<p>Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templat…'</p>
<p><b>New page</b></p><div><table border="0" cellpadding="5" align="center"><br />
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[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates##Complete_Elliptic_Integrals]]<br />
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<math>~K(\mu)</math><br />
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<math>~=</math><br />
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<math>~<br />
\ln \frac{4}{k^'} + \frac{1}{2^2}\biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} \biggr){k'}^2<br />
+ \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} \biggr){k'}^4<br />
+ \biggl( \frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} - \frac{2}{5\cdot 6} \biggr){k'}^6 + \cdots<br />
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[http://www.mathtable.com/gr/ Gradshteyn &amp; Ryzhik (1965)], &sect;8.113.3<br />
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where: &nbsp; <math>~k^' \equiv (1 - \mu^2)^{1 / 2}</math><br />
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Tohline