Difference between revisions of "User:Tohline/Math/EQ Toroidal01"
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(Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templat…') |
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[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates# | [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions]] | ||
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<math>~ | <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) | 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> | </math> | ||
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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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<math>~\psi</math> real | <math>~\psi</math> real | ||
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</table> | </table> | ||
Latest revision as of 21:37, 1 July 2018
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<math>~ Q_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi] </math> |
<math>~=</math> |
<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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A. Erdélyi (1953): Volume I, §3.11, p. 169, eq. (4) |
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| Valid for: |
<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 |