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Template:Math/EQ PplusHalf01 - Revision history
2026-04-25T13:26:11Z
Revision history for this page on the wiki
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Joel2: Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> link=Appendix/SpecialFunctions#Toroidal_Function_Evaluations </td> <td align="right"> <math>P_{+ \frac{1}{2}}(z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> \frac{2}{\pi} \biggl[z + \sqrt{ z^2-1} \biggr]^{1 / 2} ~E\biggl( \sqrt{ \frac{2(z^2-1)^{1 / 2}}{z + (z^2-1)^{1 / 2}}} \biggr) </math> </td> <td align="center" rowspa..."
2024-06-29T22:07:39Z
<p>Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <a href="/JETohline/index.php/File:LSUkey.png" title="File:LSUkey.png">25px|link=Appendix/SpecialFunctions#Toroidal_Function_Evaluations</a> </td> <td align="right"> <math>P_{+ \frac{1}{2}}(z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> \frac{2}{\pi} \biggl[z + \sqrt{ z^2-1} \biggr]^{1 / 2} ~E\biggl( \sqrt{ \frac{2(z^2-1)^{1 / 2}}{z + (z^2-1)^{1 / 2}}} \biggr) </math> </td> <td align="center" rowspa..."</p>
<p><b>New page</b></p><div><table border="0" cellpadding="5" align="center"><br />
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[[Image:LSUkey.png|25px|link=Appendix/SpecialFunctions#Toroidal_Function_Evaluations]]<br />
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<math>P_{+ \frac{1}{2}}(z)</math><br />
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<math>=</math><br />
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<math><br />
\frac{2}{\pi} \biggl[z + \sqrt{ z^2-1} \biggr]^{1 / 2} ~E\biggl( \sqrt{ \frac{2(z^2-1)^{1 / 2}}{z + (z^2-1)^{1 / 2}}} \biggr) <br />
</math><br />
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<td align="center" rowspan="2" width="20%">&nbsp; &nbsp; &nbsp; for example &hellip;</td><br />
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<math>P_{+ \frac{1}{2}}(\cosh\eta)</math><br />
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<math>=</math><br />
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<math><br />
\frac{2}{\pi}~e^{\eta/2}~ E( \sqrt{1-e^{-2\eta}} )<br />
</math><br />
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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 &amp; Stegun (1995)], p. 337, eq. (8.13.5)<br />
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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 &amp; Stegun (1995)], p. 337, eq. (8.13.6)<br />
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Joel2