Compute the Wigner 3j symbol using the Racah formula.
W = Wigner3j( J123, M123 )
J123 = [J1, J2, J3], with the condition: Ji - Jj <= Jk <= (Ji + Jj) (i,j,k are permutations of 1,2,3) M123 = [M1, M2, M3], with the conditions: Mi <= Ji (i = 1,2,3) M1 + M2 + M3 = 0 All Ji and Mi have to be half integers (correspondingly).
Reference: Wigner 3j-Symbol entry of Eric Weinstein's Mathworld: http://mathworld.wolfram.com/Wigner3j-Symbol.html
Inspired by Wigner3j.m by David Terr, Raytheon, 6-17-04 (available at www.mathworks.com/matlabcentral/fileexchange).
By Kobi Kraus, Technion, 25-6-08.
Syntax
wigner = Wigner3j( j123, m123 )
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/Wigner3j.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.