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Template:Math/EQ Toroidal04 - Revision history
2026-04-20T21:18:00Z
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https://tohline.education/SelfGravitatingFluids/index.php?title=Template:Math/EQ_Toroidal04&diff=847&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..."
2021-07-18T20:37:52Z
<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>(\nu - \mu + 1)P^\mu_{\nu + 1} (z)</math><br />
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<math>=</math><br />
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<math><br />
(2\nu + 1)z P_\nu^\mu(z) - (\nu + \mu)P^\mu_{\nu-1}(z)<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. 334, eq. (8.5.3)<br />
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NOTE: <math>Q_\nu^\mu</math>, as well as <math>P_\nu^\mu</math>, satisfies this same recurrence relation.<br />
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Jet53man