  Gaussian radial basis functions can be an accurate basis for multivariate
interpolation. In practise, high accuracies are often achieved in the flat
limit where the interpolation matrix becomes increasingly ill-conditioned.
Stable evaluation algorithms have been proposed by Fornberg, Larsson & Flyer
based on a Chebyshev expansion of the Gaussian basis and by Fasshauer & McCourt
based on a Mercer expansion with Hermite polynomials. In this paper, we propose
another stabilization algorithm based on Hermite polynomials but derived from
the generating function of Hermite polynomials. The new expansion does not
require a complicated choice of parameters and offers a simple extension to
high-dimensional tensor grids as well as a generalization for anisotropic
multivariate basis functions using the Hagedorn generating function.
