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MathGroup Archive 2000

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Re: Associated Legendre Definition

  • To: mathgroup at
  • Subject: [mg25641] Re: Associated Legendre Definition
  • From: Hendrik van Hees <h.vanhees at>
  • Date: Wed, 18 Oct 2000 02:52:18 -0400 (EDT)
  • Organization: GSI Darmstadt
  • References: <8se9qf$>
  • Sender: owner-wri-mathgroup at

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
D-64291 Darmstadt

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