User:Tohline/Math/EQ Toroidal07

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LSU Key.png

<math>~P_\nu^{\mu + 1}(z)</math>

<math>~=</math>

<math>~ (z^2-1)^{-\frac{1}{2}} \{ (\nu - \mu) z P^\mu_\nu(z) - (\nu + \mu)P^\mu_{\nu - 1}(z)\} </math>

Abramowitz & Stegun (1995), p. 333, eq. (8.5.1)

NOTE: <math>~Q_\nu^\mu</math>, as well as <math>~P_\nu^\mu</math>, satisfies this same recurrence relation.