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We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher---Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher---Bingham distribution.

Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables