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Template:Math/EQ Toroidal08 - Revision history
2026-04-19T10:16:08Z
Revision history for this page on the wiki
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https://tohline.education/SelfGravitatingFluids/index.php?title=Template:Math/EQ_Toroidal08&diff=851&oldid=prev
Jet53man: Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> Image:LSUkey.png|25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Le..."
2021-07-18T20:52:32Z
<p>Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> Image:LSUkey.png|25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Le..."</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/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions]]<br />
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<math><br />
Q_{-\frac{1}{2}}^\mu(z) + 2\sum_{n=1}^\infty Q^\mu_{n-\frac{1}{2}}(z) \cos(n\nu)<br />
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<math>=</math><br />
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<math><br />
e^{i\mu\pi}~\biggl(\frac{\pi}{2} \biggr)^{1 / 2} \Gamma(\mu + \tfrac{1}{2})\biggl[ \frac{(z^2-1)^{\mu/2}}{(z - \cos\nu)^{\mu + \frac{1}{2}}} \biggr]<br />
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[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erd&eacute;lyi (1953)]:&nbsp; Volume I, &sect;3.10, p. 166, eq. (3) <br />
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<td align="right">Valid for: &nbsp; &nbsp;</td><br />
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<math>\mathrm{Re}~\mu > - \tfrac{1}{2}</math><br />
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Jet53man