[Help-gsl] Wigner d-matrix

[Jesse Johnson]

Hello all,

While it seems most of contribs/wigner.h was ported to 
specfunc/gsl_sf_coupling.h, the Wigner (small) d-matrix was not. Indeed, 
the wigner_drot function seems to be the only reason for keeping the 
contribs file around. Is there a particular reason this function has not 
been ported? If not, what would porting it entail?

I assume the main obstacle is adding tests and verifying the 
implementation. As-is, simply copy/pasting the files into specfunc/, 
renaming them according to gsl convention, and adding the necessary 
lines to specfunc/Makefile.ac allows me to compile wigner.h into the 
library as-is.

I manually tested the function via a wrapper I wrote in Julia and was 
able to reproduce the expected results for j = 1/2, 1, 3/2, and 2 (i.e. 
j = int 1, 2, 3, 4 according to the parameter convention of multiplying 
by two to get an integer). All results were as expected based on the 
analytic formula on Wikipedia: 
https://en.wikipedia.org/wiki/Wigner_D-matrix#List_of_d-matrix_elements

For example, for j = m' = m = 3/2 (i.e., int 3) and theta = 3/4 * pi:

julia> theta = 3/4 * pi
julia> (1 + cos(theta)) / 2 * cos(theta/2)
0.05604269114599566
julia> sf_wigner_drot(3, 3, 3, theta)
0.05604269114599567

It seems strange to have the Wigner coefficients but not the rotation 
matrix, and I am sure others would find it useful, so please consider 
allowing this addition.

Thank you,

Jesse Johnson

Ph.D. candidate
Institute for Quantitative Biomedicine @ Rutgers University (address@hidden)