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A Compact Formula for Rotations as Spin Matrix Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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Group elements of $\mathrm{SU}(2)$ are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.
Keywords: spin matrices; matrix exponentials. 
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Thomas L. Curtright; David B. Fairlie; Cosmas K. Zachos. A Compact Formula for Rotations as Spin Matrix Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a83/

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