Difference between revisions of "User:Tohline/Math/EQ Toroidal01"

From VistrailsWiki
Jump to navigation Jump to search
Line 3: Line 3:
<tr>
<tr>
<td align="right">
<td align="right">
[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Toroidal_Function_Relatioinships]]
[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Special_Function_Relatioinships]]
</td>  
</td>  
   <td align="right">
   <td align="right">

Revision as of 04:07, 13 June 2018

LSU Key.png

<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>

A. Erdélyi (1953):  Volume I, §3.11, p. 169, eq. (4)

Valid for:    

<math>~t, t^'</math>  real

       

<math>~1 < t^' < t</math>

       

<math>~\nu \ne -1, -2, -3, </math> …

       

<math>~\psi</math>   real.