Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over Un, the surface of an n-dimensional hyper-sphere. Explicit formulas for the weights are given for odd degrees 3-13. The new rules are efficient and only moderately unstable. Two randomization methods are described. © 2003 Elsevier B.V. All rights reserved.
Genz, A. (2003). Fully symmetric interpolatory rules for multiple integrals over hyper-spherical surfaces. Journal of Computational and Applied Mathematics, 157(1), 187–195. https://doi.org/10.1016/S0377-0427(03)00413-8