Template:Math/EQ Toroidal02

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Revision as of 18:55, 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>Q_{n-1 / 2}^m (\lambda)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>(-1)^n \frac{\pi^{3/2}}{\sqrt{2}~ \Gamma(n-m+1 / 2)} (x^2-1)^{1 / 4} P_{m-1 / 2}^n(x) \, , </math> </td> </tr> <tr> <td align="center...")

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	$Q_{n - 1 / 2}^{m} (λ)$	$=$	$(- 1)^{n} \frac{π^{3 / 2}}{\sqrt{2} Γ (n - m + 1 / 2)} (x^{2} - 1)^{1 / 4} P_{m - 1 / 2}^{n} (x),$
Gil, Segura, & Temme (2000): eq. (8)

where:

$λ \equiv x / \sqrt{x^{2} - 1}$

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