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User:Tohline/Math/EQ Toroidal05 - Revision history
2026-05-01T16:05:39Z
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Tohline at 21:39, 1 July 2018
2018-07-01T21:39:36Z
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Tohline
https://www.vistrails.org//index.php?title=User:Tohline/Math/EQ_Toroidal05&diff=15876&oldid=prev
Tohline at 22:49, 29 June 2018
2018-06-29T22:49:22Z
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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="center" colspan=4></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="center" colspan=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>[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erd&eacute;lyi (1953)]:&nbsp; Volume I, &sect;3.12, p. 169, eq. (<del style="font-weight: bold; text-decoration: none;">xxx</del>) </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>[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erd&eacute;lyi (1953)]:&nbsp; Volume I, &sect;3.12, p. 169, eq. (<ins style="font-weight: bold; text-decoration: none;">1</ins>) </div></td></tr>
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Tohline
https://www.vistrails.org//index.php?title=User:Tohline/Math/EQ_Toroidal05&diff=15875&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…'
2018-06-29T22:47:46Z
<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#Special_Function_Relationships]]<br />
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<math>~<br />
\int_a^b\biggl[(\nu - \sigma)(\nu + \sigma + 1) + (\rho^2 - \mu^2)(1 - z^2)^{-1} \biggr] w_\nu^\mu ~w_\sigma^\rho ~dz<br />
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<math>~=</math><br />
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<math>~<br />
\biggl[<br />
z(\nu-\sigma) w_\nu^\mu ~w_\sigma^\rho + (\sigma+\rho) w_\nu^\mu ~ w_{\sigma-1}^\rho - (\nu + \mu) w_{\nu - 1}^\mu ~w_\sigma^\rho<br />
\biggr]_a^b <br />
</math><br />
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[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erd&eacute;lyi (1953)]:&nbsp; Volume I, &sect;3.12, p. 169, eq. (xxx) <br />
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<td align="right">where, <math>~w_\nu^\mu(z)</math> and <math>~w_\sigma^\rho(z)</math> denote any solutions of Legendre's differential equation</td><br />
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Tohline