Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2000
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Associated Legendre Definition
  • Next by Date: Change objetive function in Non-Linear Fit
  • Previous by thread: Re: Associated Legendre Definition
  • Next by thread: Re: Associated Legendre Definition