Template:Math/EQ Toroidal01 - Revision history

Joel2: Created page with "

link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions $Q_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi]$ $=$ $Q_\nu(t) P_\nu(t^') + 2\sum_{n=1}^\infty (-1)^n Q^n_\nu(t) P^{-n}_\nu(t^') \cos(n\psi)$ ..."
2024-06-29T21:43:43Z

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_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi] </math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> Q_\nu(t) P_\nu(t^') + 2\sum_{n=1}^\infty (-1)^n Q^n_\nu(t) P^{-n}_\nu(t^') \cos(n\psi) </math>..."

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[[Image:LSUkey.png|25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions]]
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Q_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi]
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<math>=</math>
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Q_\nu(t) P_\nu(t^') + 2\sum_{n=1}^\infty (-1)^n Q^n_\nu(t) P^{-n}_\nu(t^') \cos(n\psi)
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[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erdélyi (1953)]:  Volume I, §3.11, p. 169, eq. (4)
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<td align="right">Valid for:    </td>
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<math>t, t^'</math>  real
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<math>1 < t^' < t</math>
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<math>\nu \ne -1, -2, -3, </math> …
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<math>\psi</math>   real
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