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## [Help-gsl] Wigner d-matrix

 From: Jesse Johnson Subject: [Help-gsl] Wigner d-matrix Date: Wed, 11 Nov 2015 16:19:17 -0500 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.3.0

```Hello all,

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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?
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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.
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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
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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

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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.
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Thank you,

Jesse Johnson

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

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