Template:Math/EQ Toroidal06

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Revision as of 19:50, 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>(\xi - z)\sum_{m=0}^n (2m+1)P_m(z) Q_m(\xi)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 - (\ell+1)[P_{\ell+1}(z) Q_\ell(\xi) - P_\ell(z)Q_{\ell+1}(\xi)] </math> </td> </tr> <tr> <td align="center"...")

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	$(ξ - z) \sum_{m = 0}^{n} (2 m + 1) P_{m} (z) Q_{m} (ξ)$	$=$	$1 - (ℓ + 1) [P_{ℓ + 1} (z) Q_{ℓ} (ξ) - P_{ℓ} (z) Q_{ℓ + 1} (ξ)]$
Abramowitz & Stegun (1995), p. 335, eq. (8.9.2)

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