Treffer: Approximation of hypergeometric functions with matricial argument through their development in series of zonal polynomials

Hypergeometric series of matrix argument, defined in terms of zonal polynomials of positive definite matrices, are considered here. An algorithm is given to compute the first few terms of the series, which provide an approximation to the series. Explicit evaluations are given for Gauss hypergeometric series involving \(2\times 2\) matrices.