Other methods include numerical quadrature applied to double and multiple
integral representations. See Yan (1992) for the
and functions of matrix argument in the case , and
Bingham et al. (1992) for Monte Carlo simulation on applied to a
generalization of the integral (35.5.8).
Koev and Edelman (2006) utilizes combinatorial identities for
the zonal polynomials to develop computational algorithms for
approximating the series expansion (35.8.1).
These algorithms are extremely efficient, converge rapidly
even for large values of , and have complexity linear in .