Difference between revisions of "User:Tohline/Math/EQ Toroidal01"
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<td align="left"> | <td align="left"> | ||
<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> | ||
</td> | </td> | ||
| Line 48: | Line 48: | ||
</td> | </td> | ||
<td align="left"> | <td align="left"> | ||
<math>~\psi</math> real | <math>~\psi</math> real | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
Revision as of 19:42, 19 June 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 |