Template:Math/EQ Toroidal04

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Revision as of 18:22, 29 June 2024 by Joel2 (talk | contribs) (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math>(\nu - \mu + 1)P^\mu_{\nu + 1} (z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> (2\nu + 1)z P_\nu^\mu(z) - (\nu + \mu)P^\mu_{\nu-1}(z) </math> </td> </tr> <tr> <td align="center" colspan="4"> [https://...")
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(νμ+1)Pν+1μ(z)

=

(2ν+1)zPνμ(z)(ν+μ)Pν1μ(z)

Abramowitz & Stegun (1995), p. 334, eq. (8.5.3)

NOTE: Qνμ, as well as Pνμ, satisfies this same recurrence relation.