The efficient evaluation of the hypergeometric function of a matrix argument

@article{Koev2006TheEE,
title={The efficient evaluation of the hypergeometric function of a matrix argument},
author={Plamen Koev and Alan Edelman},
journal={Math. Comput.},
year={2006},
volume={75},
pages={833-846}
}

We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.