spherical.recursions.wignerH

Source: spherical/recursions/wignerH.py

Algorithm for computing H, as given by arxiv:1403.7698 H is related to Wigner's (small) d via dₗⁿᵐ = ϵₙ ϵ₋ₘ Hₗⁿᵐ, where ⎧ 1 for k≤0 ϵₖ = ⎨ ⎩ (-1)ᵏ for k>0 H has various advantages over d, including the fact that it can be efficiently and robustly valculated via recurrence relations, and the following symmetry relations: H^{m', m}_n(β) = H^{m, m'}_n(β) H^{m', m}_n(β) = H^{-m', -m}_n(β) H^{m', m}_n(β) = (-1)^{n+m+m'} H^{-m', m}_n(π - β) H^{m', m}_n(β) = (-1)^{m+m'} H^{m', m}_n(-β) Because of these symmetries, we only need to evaluate at most 1/4 of all the elements.