Re: Associated Legendre Definition
- To: mathgroup at smc.vnet.net
- Subject: [mg25641] Re: Associated Legendre Definition
- From: Hendrik van Hees <h.vanhees at gsi.de>
- Date: Wed, 18 Oct 2000 02:52:18 -0400 (EDT)
- Organization: GSI Darmstadt
- References: <8se9qf$6q3@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Preben Bohn wrote: > P(n,m,x) = (1-x^2)^(m/2) d^m/dx^m (P(n,x)) It's just the problem that there are many different conventions around. The associated Legendre Polynoms are defined up to a factor of modulus 1. That's clear if you think about them as eigenfunctions of the Casimir operator of the rotation group SO(3) in quantum mechanics (orbital angular momentum squared) and the 3-component of the angular momentum. Y_l^m(theta,phi)=exp(i m phi) P_l^m(cos(theta)) l=0,1,2,... and for given l: m=-l,-l+1,...,l-1,l -- Hendrik van Hees Phone: ++49 6159 71-2751 c/o GSI-Darmstadt SB3 3.183 Fax: ++49 6159 71-2990 Planckstr. 1 mailto:h.vanhees at gsi.de D-64291 Darmstadt http://theory.gsi.de/~vanhees/index.html