Difference between revisions of "User:Tohline/Math/EQ Toroidal08"
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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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Revision as of 21:40, 1 July 2018
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<math>~ Q_{-\frac{1}{2}}^\mu(z) + 2\sum_{n=1}^\infty Q^\mu_{n-\frac{1}{2}}(z) \cos(n\nu) </math> |
<math>~=</math> |
<math>~ e^{i\mu\pi}~\biggl(\frac{1}{2\pi} \biggr)^{1 / 2} \Gamma(\mu + \tfrac{1}{2})\biggl[ \frac{(z^2-1)^{\mu/2}}{(z - \cos\nu)^{\mu + \frac{1}{2}}} \biggr] </math> |
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A. Erdélyi (1953): Volume I, §3.10, p. 166, eq. (3) |
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| Valid for: |
<math>~\mathrm{Re}~\mu > - \tfrac{1}{2}</math> |