User:Tohline/Math/EQ Toroidal08

From VistrailsWiki
< User:Tohline
Revision as of 22:46, 1 July 2018 by Tohline (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

LSU Key.png

<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{\pi}{2} \biggr)^{1 / 2} \Gamma(\mu + \tfrac{1}{2})\biggl[ \frac{(z^2-1)^{\mu/2}}{(z - \cos\nu)^{\mu + \frac{1}{2}}} \biggr] </math>

A. Erdélyi (1953):  Volume I, §3.10, p. 166, eq. (3)

Valid for:    

<math>~\mathrm{Re}~\mu > - \tfrac{1}{2}</math>